Example 2: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. This can be easily be calculated using D’morgans Law, i.e. How to solve questions based on At least n in Set Theory for CAT Exam? Do you see that alex, casey, drew and hunter are in the "Soccer" set? But you can easily solve them using little manipulation and basic addition and subtraction. A Venn diagram is a diagram that shows all possible logical relations between a finite collection of sets. DIFFERENCE OF SETS: If A and B are two sets then their difference (A – B) is a set containing elements that are only present in A and not in B. If a1 + a2 + ….+a3n = 1830, then what is the smallest positive integer m such that m (a1 + a2 + …. Set Theory- Maximum and Minimum Values A Venn diagram is also known asa Primary diagram, Set diagram or Logic diagram. And then we can do interesting things like take the whole set and subtract the ones who play Soccer: U − S = {blair, erin, francis, glen, ira, jade}, Which says "The Universal Set minus the Soccer Set is the Set {blair, erin, francis, glen, ira, jade}". Let's say that our universe contains the numbers 1, 2, 3, and 4, so U = {1, 2, 3, 4}. How many candidates had none of the three? The Universal Set is the set that has everything. Mathematically, A ∩ B = {x: x Є A and x Є B}. Your email address will not be published. (exactly the same as the U − S example from above), {alex, blair, casey, drew, erin, francis, glen, hunter, ira, jade}. We can put their names in two separate circles: You can now list your friends that play Soccer OR Tennis. The objects could be anything numbers, letters, vectors, etc. Let’s construct the table like we did earlier in 3 set Venn diagram case corresponding to the value of the region. Javascript on your browser is not enabled. If the sum a1 + a2 + a3 +……. A set is generally denoted with a capital alphabet S or A or and its elements are generally enclosed in curly brackets like this S = {2, 3 ,4} Here, 2, 3 and 4 are elements of set S and an element is generally denoted using the symbol Є (belongs to) like this: 2 Є S. When a set is very large and cannot be contained it can also be denoted in the following way: A = {x: x is an integer} or, B = {x:0 Only Players = 25. Thus, if B is contained in S then it can be written as B ⊂ S. A = {x: x<5, x Є Z+} and B = {1, 2, 3, 4}, Notice that both the sets are equal as A = {1, 2, 3, 4}. It is a very basic and easy concept but has significant use in Algebra, Logic, Combinatorics, probability etc. And that casey, drew and jade are in the "Tennis" set? We show it by writing a little "C" like this: Which means "everything that is NOT in S", like this: Sc = {blair, erin, francis, glen, ira, jade} Your IP: 207.180.252.68 20000+ students have used our online courses from 50+ cities in India. Doctors that are both Artist and Players => D ∩ A ∩ P = 3, 3.) There can be many questions formed on these kinds of sets. How many can speak French only and how many can speak both English and French? Home » Blog » Basics of Set Theory with Venn Diagrams. Various Relationship between sets using Venn Diagrams, Also, notice that through the Venn diagram that A -B = A ∩ B’, n(A B C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C), Let A, B and C be three sets and U be the universal set then the Venn diagram for 3 sets can be constructed as following. The above diagram is called Venn Diagram where there are two sets A and B and U is the universal set. alex and hunter play Soccer, but don't play Tennis or Volleyball, Empty Set: the set with no elements. Performance & security by Cloudflare, Please complete the security check to access. A Venn diagram, also called primary diagram, set diagram or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets. The set is denoted by the symbol. Sol: Let A denote candidates who have 2-wheelers. How to find Rank of a Word in Dictionary (With or Without Repetition) Here, 2, 3 and 4 are elements of set S and an element is generally denoted using the symbol Є (belongs to) like this: 2 Є S. When a set is very large and cannot be contained it can also be denoted in the following way: B = {x: 0