# Tips and Tricks and Shortcuts for Set Theory

## Shortcuts for Set theory

set is a collection of some items (elements). To define a set we can simply list all the elements in curly brackets. This page is all about Tips and Tricks for Set Theory. Using tips and tricks your task will become easier and you will be able to solve these questions easily. We have added some examples also  for your better understanding

### Tips and Tricks For Set Theory

Question 1 – In an examination hall with 60 students, their identity cards were examined. Some of them were not having Id card, some of them did not had admit card and some people were not  having both of them. The If 20 people were having Id card and about 10 people had both, how many people did not had  id  and how many people did not had admit card?

Answer: People having only Id card=n(A)={20-10}= 10
People having only admit card= n(B) = {20-10}=10
Let n(S) be:
People having None =n(A)-n(B) = {60-20}= 40 Ans.

Question 2: If set A ={1,2,3,4} set B={3,6,7,8} and set C={6,7,8,9} then write the universal set for all the three sets?

Answer: If U is universal then U must contain Elements of set A + set B + set C
U={1,2,3,4,6,7,8,9}

Question 3: If A= { X,Y,A,B} B= {T,U,V,X} C= {T,M,N,B}  then find (A ∩ B) ∩ ( B  C).

Answer: (A ∩ B) = {X}
( B  C)= {T,U,V,X,M,N,B}
(A ∩ B) ∩ ( B  C)= {X} .

Question 4: Given set A={9,0} B={9,0,18,27,36} Is A⊂ B? Find AB.

Answer: Yes  AB as elements of A are present In B. AB= {9,0}

Question 5: In a classroom 10 students has Computer as optional subject and 30 student has Physical education as their optional subject and rest all others have Sanskrit find the number of students who have sanskrit as optional subject if the total number of student in class are 60?

Answer : Set A = Student with CS{10}

Set B = Student with PE {30}

Other students = n(A)+n(B)-n(U) = 10+30-60= 20

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