Terms Beginning With 'v'

Venn Diagram

  • January 07, 2020
  • Team Kalkine

What is a Venn Diagram?

A Venn diagram is a graphical representation that shows the relationship between a finite group of things. In a Venn diagram, the relationship between the group of things, called sets, is explained with the help of circles.

In case there is something common between two sets of data, then the circles would overlap. On the other hand, if the two sets of data are distinct, the circles will not overlap.

Let us take an example to understand the concept:

Suppose A is a set of numbers that are divisible by 2 and B is a set of numbers that are divisible by 3. In these two sets, there would be some common numbers as well, which are divisible by both 2 and 3.

A= {2, 4, 6, 8,10, 12, 14, 16, 18, 20}

B= {3,6,9,12,15,18,21,24,27,30}

Graphically the above statement is interpreted using a Venn Diagram as below:

The yellow region represents numbers that are only divisible by 2 while blue represents those numbers that are divisible 3 only. The section highlighted in green describes the numbers that are multiples of both 2 and 3.

Mathematically,

  • (A U B), or A union B, comprises all the numbers from sets A and B.

(A U B) = {2,3,4,6,8,9,10,12,15,16,18,20,21,24,27,30}

  • (A ∩ B), or A intersection B, represents the numbers common for both sets A and B.

(A ∩ B) = {6,12,18,24,30}

Sets and Venn Diagrams:

A set is defined as a list of elements. In other words, it is the grouping of individual elements into a whole. It is essential to understand that the elements are clear and unambiguous.

An example of an unclear set: {set of tall boys}

An example of an unambiguous set: {set of even numbers less than 20}

What are the different types of sets?

  1. Singleton set: Singleton set has only one element within the set.
  2. Finite set: Finite set has a limited number of objects. E.g., set of numbers divisible by 2 and less than 20.
  3. Infinite set: A set of rational numbers between 0 and 1. This is an example of an infinite set.
  4. Equal set: If two sets have the same elements, then we say that two sets are equal.
  5. Null or Empty set: Null or empty set has no element.
  6. Subset: If we say that ‘A’ is a subset of ‘B’, then it means that each element of set A is there in set B. The subset is represented using symbol “?”.
  7. Proper set: Set A is a proper subset of B if A is a subset of B and A is not equal to B. It can also be described as A is a subset of B; however, B has at least one such element which is not a part of A.
  8. Improper set: In improper subset, A is said to be an improper subset of B if A=B.
  9. Power set: Power set refers to all possible combination of sets. E.g.: A={1,2}, then P(A)= {{}.{1}, {2},{1,2})
  10. Universal set: Universal set is the superset of all the subsets under consideration.

How do Venn Diagrams help users?

As described above, a set describes a group of elements which are represented within curly brackets ({, }). Now suppose there are three sets, and we want to understand if there exists a relationship between these sets. In such a scenario, Venn diagrams prove useful.

Now, the question which arises here is that how we can establish a relationship between these sets. The relationship between the sets can be understood through various symbols, as discussed below.

To understand the relationship, let us consider an example where there are two sets of players from cricket and football. Students is the set of all students studying in a class (universal set).

Students = {A, B, C, D, E, F, G, H, I, J, K, L,M}

Cricket = {A, B, C, D, E, F}

Football= {E, F, G, H, I, J}

Union (?)

In Union, the elements of two or more sets are combined. Now, if we want to know the name of all those students playing cricket or football or both, then we use union. So, we represent that the set of students playing cricket or football, or both are:

Cricket ? Football = {A, B, C, D, E, F, G, H, I, J}

Through the Venn diagram, “Cricket ? Football” includes those students that either play cricket or football or both (area highlighted in pink).

Intersection (∩):

In an intersection, the set comprises of these elements which are common in both the sets. In this case, two students are playing both cricket and football.

Cricket ∩ Football = {E, F}

Through the Venn diagram, “Cricket ∩ Football” includes those students highlighted in the pink region.

Difference (-):

In simple terms, a difference in mathematics means to subtract. So, if we say Cricket – Football, then the set would include only those players who are playing cricket and not football.

Cricket – Football = {A, B, C, D}

Through the Venn diagram, “Cricket – Football” includes those students highlighted in the pink region.

Compliment (S’ or Sc, where S is set):

If we say Footballc or Football compliment, it means that the set would include all the students in the classroom who are not playing football at all.

In this case,

Footballc = {A, B, C, D, K, L,M}

Through the Venn diagram, “ Footballc “  includes those students highlighted in the pink region.

Applications of Venn Diagram:

Some cases where Venn Diagrams can be useful include:

  • Observing a Student's Behaviour
  • Understanding the interaction of the students in the class
  • Marketing analysis
  • Tracking the health of the patient
  • Support in identifying the respective responsibilities of state and federal government

 What is Game Theory? Game theory is a mathematical statistical analysis of how individuals react to different circumstances presented to them. Each situation comes with a set of payoffs and the individuals must decide which move to play based on these expected playoffs. Since these payoffs are known to the players depending on different moves by all the participants, the entire course of action depends on the strategy chosen by the players. This strategy might be incentivising for one and harmful for the other or can be beneficial to both. Thus, the players must decide whether to collaborate, or to work for their own profits. The concept of game theory has various applications in real life. A game theory set up can help alter an individual’s strategy based on his assumptions about the opponent’s move. Thus, it helps determine a sustainable outcome in a situation where two individuals find themselves at conflict. However, not all game theory set ups can be solved productively as they involve trade-offs between what the players desire.  What are the different terms used in game theory analysis? PLAYERS: There are two players in most game theory experiments, and each player is affected by the strategy played by both the players. PAYOFFS: Payoffs refer to the outcomes for each player of the game based on different strategies. A payoff matrix depicts the different situations and the associated outcomes by both the players in a diagram form. STRATEGY: It refers to the course of action adopted by the players depending on the payoff matrix known by them. It can be for personal profit or in collaboration with each other. INFORMATION SET: The players are aware about the possible strategies and the payoffs attached to them. This information forms the information set which is used by the players to choose their moves. What is Nash Equilibrium? Nash equilibrium refers to that outcome in the game in which both players have achieved the best possible solution through a collaboration. This is the state from which neither of the players would want to deviate. This outcome may not always be optimal for both. In certain instances, it might be possible to make one player better off by making the other worse off. What is Pareto Optimality? Pareto Optimality refers to that stage in which both players have reached their best potential. This state considers the individual’s best outcome rather than the collaborative best outcome. Thus, it is that state from which it is not possible to make one player better off without making the other worse off. The outcome for both the players is at its best. A Nash equilibrium may not always be pareto optimal. This means that the outcome which is the collaborative best between both players may not be pareto optimal. Thus, it is possible to deflect from that outcome and make both players reach their personal best. What are the different types of strategies used by the players? The strategies in the game can be of two types: Pure Strategy: This is the strategy which is fully defined for a player and can be thought of as ‘occurring with full probability’. Mixed Strategy: This involves assigning probabilities to pure strategies. This allows players to randomly choose a pure strategy. Thus, pure strategy can be termed as a mixed strategy occurring with probability equal to 1. How is the concept of game theory applied? Prisoner’s Dilemma: The most common application of Game Theory can be seen in the example of Prisoner’s Dilemma. This game involves two prisoners who are not aware about each other’s decisions in the game. Both have been suspected of committing a crime and are held for questioning. The prisoners face different years of jail sentence based on the strategy they choose. The payoff matrix is as follows:   Here the Nash Equilibrium is achieved when both A and B confess. Thus, (5,5) is the collaborative best that both the players can perform. However, this is not the pareto optimal solution. The pareto optimal outcome is (1,1) as both players want to serve as less jail time as possible. Thus, it is not possible for one to be better off without making the other worse off if neither one of them confesses.   Battle of the Sexes: Battle of the sexes is a game where a girl and a boy want to go on an outing together, however the girl prefers going to see an opera while the boy prefers going to a football match. However, going to these places separately does not earn them any payoffs, while going together gives higher payoff to only one of them and not both.   The payoff matrix is as follows: There are two possible Nash equilibria in this game. One is achieved when both go to Opera and the other when they both go to watch the Football match. Is the concept of game theory accurate? The limitation of game theory is that it is based on certain assumptions. It assumes that the players would always act in favour of their personal interests. However, it is possible to witness real life scenarios where people are more collaborative as well as altruistic. It is also possible that in a real life set up, stability is achieved at an outcome which is not a Nash Equilibrium. Depending on the varied social set ups as well as personal preferences, game theory may not always justify real life situation.

What is XML (Extensible Markup Language)? XML (Extensible Markup Language) is a text-based markup language. It is derived from SGML or Standard Generalized Markup Language. XML tags, unlike HTML tags, detect the data and are used for storing and managing data.           What are the characteristics of XML? XML is extensible. It means that there is a possibility that you can build your self-descriptive tags/languages that fits your application. XML allows the user to store data irrespective of the way it is presented. This is one of the advantages XML has over HTML. World Wide Web Consortium developed XML and is available as an open standard. XML is used to store & transport data. XML tags are self-descriptive. The markup language is used to carry data. In HTML, we display data in a presentable way. Through XML, we can carry this data from one application to another. XML tags are self-defined. The language is platform and language independent. It means that whatever application you use like Java or through an oracle, there would be no impact on the XML page. Facilitates easy communication between two platforms. What are the Advantages of XML? Separate data from HTML (HyperText Markup Language) Simplifies data sharing Increases data availability XML simplifies platform change. For example, if you have a data on SQL server and want to import to oracle server, then it can be made possible through XML. An Example to explain XML A simple code to represent the above hierarchical structure in XML: //*{mandatory line to start xml and is called declaration}//* <?xml version= ”1.0” encoding = “ ISO-8859-1” ?>   <college> <class 1> <name> ABC</name> <roll> 01 </roll> </class 1> <class 2> <name> DEF </name> <roll> 02 </roll> </college> In this code, we have created our own tags like <college> <class> <name> and <roll>.  As highlighted in the diagram as well, there is a root element, and while writing an XML code, it is mandatory to have a root element. It should be noted that the tags used in the code are case sensitive. Hence, the opening and closing tags should be in the same case (upper or lower). Also, XML is dynamic in nature. How to Import an XML file into Excel? One can import XML files in an Excel workbook to make them more readable for humans. The BI tool, Power Query makes it easy to import an XML file and transform it as per the user’s requirements. Suppose you save the XML file mentioned above on your system as student.xml. To import the file, follow the steps mentioned below: Open excel and go to Data tab in the ribbon Click get data Select from the file Select From XML A window will open. Go to the folder where the file is saved and then click the button “Import”. In the next step, you would see that a navigator window open, and we can see a preview of data from the XML file in a table format. What is an XML map? XML maps are ways by which MS Excel (Excel) represents XML schemas within a workbook.  Excel uses maps using binding data from the XML file to cells and ranges on the worksheet. Through XML maps it is possible to export data from excel to XML. If there exists an XML map on the worksheet, the user can import data into map ant time. XML schemas describe the elements used in the XML document and can be used by the programmers to verify each item in the document. It defines an element, attributes, and data types. Through XML map, XML schema gets copied to the workbook to create map instead of referencing the schema as an external file. Using XML Maps, you can add and delete maps. Once the XML file and schema are imported in the Excel file, the user can add further details and make desired changes. The edited file can again be exported to XML. Where we develop XML code? To create and modify XML code quickly and effortlessly, we can use Microsoft XML Notepad. With this tool, the structure of the XML data is shown graphically in a tree structure. The interface presents two panes: One for the structure. One for the values. The user can add comments, attributes, elements, attributes, and text to the XML document by creating the tree structure in the left pane and entering values in corresponding text boxes. Applications that support XML import and export: RDBMS tools including IBM DB2 (pureXML), Microsoft SQL Server, Oracle Database and PostgreSQL. Machine learning tools such as R Studio, and Python.

What is meant by revaluation? Revaluation refers to deliberately exerting an upward pressure on the prices of goods, assets and even currencies. In accounts, revaluation may refer to readjustments made to the prices of commodities and assets. For a central bank, revaluation refers to applying an upward pressure to the exchange rate. Countries that maintain a fixed exchange rate can adjust the value of their currency against a baseline. This baseline can be another currency or the value of a commodity like gold. Revaluation can be understood as the opposite of devaluation, wherein countries deliberately decrease the value of their domestic currency against the baseline. Revaluation and devaluation cannot occur in a floating exchange rate system where the exchange rate is determined by market forces. In a floating exchange rate system, there is minimal to no intervention by the government or central bank of a country in increasing or decreasing the value of their currency. How is revaluation carried out? If the exchange rate of Country A is maintained at 10:1, then the home country can simply announce that the value of the domestic currency will be revalued to 2:1. This would increase the value of the domestic currency. Further, if the central bank announces that the exchange rates are being maintained at 12:1, then this is called devaluation. Countries may also choose to revalue their currency by changing the supply of foreign currency reserves in their country. Changing the supply of foreign currency affects the exchange rate. Consider the following example depicting the exchange rate determination of Dollar in terms of Euro. The supply of Euro is the quantity of Euro available as foreign exchange with the US, while the demand for Euro reflects its demand in the US. Here, Dollar is the domestic currency and Euro is the foreign currency. In the above diagram, the supply of Euro in the economy is increasing, while the demand for Euro remains the same. As more units of Euro are kept as foreign exchange, Euro depreciates while Dollar appreciates. This is how countries can influence the value of the currency by changing the supply of foreign exchange reserves. What is the effect of a revaluation? If the exchange rate of country A is maintained at 7:1, then it can be said that 7 units of domestic currency are required to get one unit of foreign currency. However, when the exchange rate is revalued to 5:1 then it means that now only 5 units of domestic currency are required to get one more unit of the foreign currency. This means that the foreign currency has lost its value as it has become cheaper, while the domestic currency has gained value as it is more expensive. Lesser units of domestic currency must be foregone to get the same amount of foreign currency. A revaluation would impact the domestic currency in the following ways: Exports become more expensive: As the value of domestic currency rises compared to a foreign currency, exports become more expensive. This would end up hurting the country as exports would decline. Imports become cheaper: Domestic consumers would prefer cheaper imports over domestic goods because the value of foreign currency is less. Thus, there would be a decline in net exports. Lower inflation: Inflation would decline as lesser amount of cash would hold greater value than before. Therefore, purchasing power of domestic currency would increase and lesser units of currency would be required to purchase the same amount of money. Lower Economic Growth: As the demand for domestic goods falls domestically as well as internationally, the overall output in the economy would also fall. This could lead to lower productivity and therefore, lower economic growth and lesser number of jobs would be available in the economy. Current Account Deficit: As imports increase and exports decline, the current account balance would decrease. This would have a negative impact on the Balance of Payments of the domestic country. Why do countries revalue their currency? Interest Rates: Interest rates are a major factor influencing the demand and supply of foreign exchange reserves with a country. As the interest rates in a country increase, there is greater demand for the currency of that country. This happens because investors would have an incentive to invest in that country rather than in their own. Interest rate changes between countries could lead to one country revaluing its currency to keep it at par. Consider the case when interest rates in the UAE are higher than in Saudi Arabia. Then the demand for UAE’s Dirham would increase, thus, Dirham would appreciate, and the Saudi Riyal would depreciate. To increase the value of the Riyal, the Saudi Arabian government, under a fixed exchange rate system, would revalue their currency. Current Account Surplus: Countries might look at revaluation when they experience a current account surplus and want to reduce it. A current account surplus could lead to lower domestic employment if it is caused by a recession or a lack of demand. Containing Inflation: Currency revaluation can be used to countries to contain inflation. Revaluation reduces the value of currency, thus, leading to a downward pressure on prices.

What is a tariff? A tariff is a tax levied on foreign goods and services imported into a country. Tariffs make goods and services more expensive and thus, consumers shift to the domestic alternatives. Tariffs are usually imposed as an economic tool to improve the balance of trade as they decrease the imports. They are also targeted at protecting the domestic producers from competitive foreign goods. Tariffs can also be imposed on exports of goods and services, although that is seldom the case. It is done to discourage exports of certain goods and services. Tariffs are also used as a political tool. Governments may sometimes favour certain countries with whom they have political ties, while they may try to limit trade with other countries owing to technological, economic and political spats. How are tariffs levied? Tariffs have three broad types based on how they are levied: Ad-Valorem Tariff: Ad valorem taxes are the taxes that are levied as a fraction of the value of goods and services. They are represented as a percentage of the total value of imports and are proportionate to the value of imports. Specific Tariff: Specific tariffs are levied per unit of quantity. Specific duties are flat fees applied over a specific quantity of goods and services. For instance, a tariff of $10 levied per 20 kgs of wheat is an example of a specific tax. This tax is proportionate to the quantity of the imported good. Compound Tarifs: Compound tariffs are a mix of both specific tariff and ad valorem taxes. For instance, a tariff that has a specific tax up to a certain amount followed by an ad valorem tax afterwards is an example of a compound tariff. What impacts can a tariff have? Import tariffs can be beneficial to an economy in many ways. As imports become expensive, consumers shift towards domestic goods. This competitive advantage enjoyed by domestic goods translates into increased production along with higher profits to domestic firms. Thus, as firms start gaining increased profits, they expand and hire more workers. This increases the overall employment in the economy. Therefore, tariffs affect two major areas positively: the domestic competitiveness of firms as well as the employment rate in the economy. Tariffs can sometimes also be implemented to protect the domestic economy from infiltration of foreign produce. Sometimes, highly developed nations impose import duties to safeguard their economies from dumping of foreign goods. This kind of tariff is called an anti-dumping duty which is used when a country is suspected of exporting a good at a rate which is lower than the rate at which the same good is sold in their domestic markets. How does a tariff work? Consider the following diagram: In the figure above, point O represents the situation of autarky or a closed economy that has no trade with foreign countries. Now consider the effects of the economy opening its borders to international trade. The international price of the same good is Pw, which is significantly lower than Pd, the domestic price. Under the assumptions of free trade and a small domestic economy, the domestic prices would also become equal to Pw. At price Pw, the domestic demand is Q4 while the domestic supply is Q1. The difference between the two is met by the quantity of imports. The lower price of the imports would make them preferable to the domestic produce. However, when a specific tariff is introduced on the imports, the price of the imported good rises to Pw + T. This makes the good more expensive and thus reduces its imports into the economy from Q1Q4 to Q2Q3. Who are the winners and losers when a tariff is implemented? The welfare implications of a tariff are a subject of popular debate. Many theorists argue that tariffs bring distortions into the economy. The red box ABCD represents the revenue earned by the government through the tariff. The line AD represents the value of tax while the link DC represents the amount of imports. The domestic prices would rise to Pw +T when the tariff is introduced. As a result, domestic consumption falls to Q3, while the domestic produce increases to Q2. Therefore, domestic producers gain from a tariff. The supply has increased from Point E to point A. The demand has come down from point F to point B. The government also gains a lumpsum amount equal to AD multiplied with DC, which is the tariff revenue. Thus, both producers and the government are gaining from a tariff. However, the entire process is giving rise to a deadweight loss which is represented through triangles AED and BCF, both coloured in blue. These two triangles are not utilised anywhere and are lost in the process of tariff implementation. Thus, there is a welfare loss associated with tariffs, that is paid by the consumers. The consumers could afford a greater amount of the good at price Pw. However, when prices are increased to PW + T, part of welfare lost by consumers goes to producers, and a part of it goes to the government. But triangles AED and BCF are lost in this process. Therefore, tariffs cause a distortion in a free market and can even lead to many adverse economic repercussions. Thus, for a small economy, tariffs need to be implemented with proper regulation and without any intent of harming any country’s producers. Rather, the intent should be to protect the domestic producers. The same might not be true for a large economy as any protectionist intent by one country can trigger a trade war between several countries as seen in a few past scenarios.

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