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August 10, 2023
Definition for Set Theory – Set Theory is a branch of Mathematics that deals with the properties of well- defined collections of an object. In other words, its natural habit for all of us to classify similar things into groups. These groups are known as Set. This page is basically to help students and help them with a query of – “How To Solve Set Theory Questions Quickly.”
We are going to provide you the best methods to solve the questions quickly. The best way to solve the question is by practicing them and before practicing we need to see the Solved Examples. Here are a few solved examples which will definitely help your query of – “How To Solve Set Theory Questions Quickly.”.
Question 1 – In a class of 100 students, 35 like science and 45 like math. 10 like both. How many students like neither of them?
OPTIONSa) 30
b) 24
c)31
d)18
Explanations – Total number of students, n(µ) = 100Number of science students, n(S) = 35Number of math students, n(M) = 45Number of students who like both, n(M∩S) = 10Number of students who like either of them,n(MᴜS) = n(M) + n(S) – n(M∩S)=> 45+35-10 = 70
Number of students who like neither = n(µ) – n(MᴜS) = 100 – 70 = 30
CORRECT ANSWER(A)
Question 2 – In a group of 60 people, 27 like tea and 42 like coffee and each person likes at least one of the two drinks. How many like both coffee and tea?
Therefore, 9 people like both tea and coffee.
CORRECT ANSWER (D)
Question 3 – Let A and B be two finite sets such that n(A) = 24, n(B) = 37 and n(A ∪ B) = 46, find n(A ∩ B).
OPTIONS
a)12
b) 15
c) 8
d) 4
Explanation
Using the formula n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
then n(A ∩ B) = n(A) + n(B) – n(A ∪ B)= 24 +37 – 46
= 61- 46= 15
CORRECT ANSWER (B)
Question 4 – A class consisted of 50 students, 20 were studious and liked to do physical activities also and 10 only liked to study how many students came under none of the above category?
b) 25
c) 30
then n(A ∩ B) = n(A) + n(B) – n(A ∪ B)= 20+10 – 10-50
= 30
CORRECT ANSWER (C)
Question 5 – In a college 500 students speak Hindi 200 speak English and 200 speak both Hindi and English, find the number of students in the college?
a)300
b) 200
c) 450
d) 500
Number of students who speak Hindi =n(H)=500
Number of students who speak English =n(E)=200
Number of students who speak both =n(HUE)=200
U=n(H)+n(E)-n(HUE)= 500+200-200=
CORRRECT ANSWER(D)
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