d In a group of 1000 people 750 can speak English and

# MCQs on Set Theory

set theory examples, set theory basics, set theory formulas, set theory problems,set theory questions

Q1. If A={x:x=2n+1, n∊Z} and B={x:x=2n, n∊Z} then A∪B is;

a. ∅

b. Z

c. R

d. None of these

Solution: Option ‘b’ is correct

Explanation:

Here clearly A is set of odd integers and B is set of even integers, so;

so, A∪B={x:x is an odd integr}∪{x:x is an even integer}=[x:xis an integer}=Z

Q.2 If A={1,3,5,7,11,13,15,17}, B={2,4,6,….,18} and N is the Universal set, then A′∪((A∪B)∩B′) is equal to;

a. A

b.B

c. N

c. φ

Solution: Option ‘c’ is correct

Explanation:

Since A and B are the disjoint sets

∴ (A∪B)∩B′=A

hence, => A′∪((A∪B)∩B′)=A′∪A=N

Q3. Two sets have m and n elements. The total number of subsets of the first is 56 more than the total number of subsets of the second set. Then the values of m and n are;

a. 6 and 3 receptively

a. 3 and 3 receptively

a. 3 and 6 receptively

a. 6 and 6 receptively

Solution: Option ‘a’ is correct

Explanation:

Let there be two sets A and B with elements m and n respectively.

Number of subsets of set A= and number of subsets of set B= It is given that A has 56 subsets more than B Taking as common; so,  so, set theory examples, set theory basics, set theory formulas, set theory problems,set theory questions

Q4. The number of proper subsets which can be formed from {x,y,z) are;

a. 8

b. 7

c. 6

d. 9

Solution: Option ‘b’ is correct

Explanation:

Number of proper subsets = Here n is the number of elements in a set

so, number of proper subsets for given set is Q5. If A={0} then number of elements in the set A²=AxA is;

a. 1

b. 0

c. 2

d. none of these

Solution: Option ‘a’ is correct

Explanation:

A={0}

so, => AxA={(0,0)}

Here (0,0) is taken as one element

Q6. If A is a set of n distinct elements then number of elements in P(A) is;
a. b. c. d. Solution: Option ‘a’ is correct

Explanation:

The set of all subsets of a set A is called its power set and is written as P(A)

If there are n elements in set A then number of its subsets is So, it means there will be subsets in P(A) or we can say there will be elements in P(A)

Q7. The only set of prime trplets among these is ;

a. {1,3,5}

b. {3,5,7}

c. {1,2,3}

d. {5,7,9}

Solution: Option ‘b’ is correct

Explanation:

so, 1 is neither prime nor composite so, only {3,5,7} is the prime triplet set

Q8. In a group of 1000 people 750 can speak English and 400 can speak Spanish. How many people can speak Spanish only ?

a. 150

b. 250

c. 350

d. 600

Solution: Option ‘ b’ is correct

Explanation:

Let A= set of those persons who speak English and B = set of those who speak Spanish

=> n(AuB) =1000, n(A)= 750 and n(B)=400

=> n(A∩B)=n(A)+n(B)-n(AuB)= 750+400-100=150

so, n(B-A)=n(B)-n(A∩B)=400-150=250

Q9. In a class of 100 students 700have taken science, 60 have taken mathematics and 40 have taken both subjects.The number of students who have not taken science or mathematics or both is;

a.90

b.10

c.30

d.20

Solution: Option ‘b’ is correct

Explanation:

Total students=100

students who took science =n(S)=70

and who took Mathematics=n(M)= 60

who took science and Math =n(S∩M)=40

Now n(SuM) = n(S)+n(M)-n(S∩M)=70+60-40=90

hence required number of students = 100-90=10

Q10. If two sets are disjoint, then their intersection is ;

a. Cartesian product

b. singleton set

c. null set

d. none of these

Solution: Option ‘c’ is correct

Explanation:

Two sets are disjoint if there is no element common in between them. So intersection will be a  null set