"> MCQs on Set Theory | Job Exam Rare Mathematics (JEMrare)

MCQs on Set Theory

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;

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

=> 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=  2^{m} and number of subsets of set B= 2^{n}

It is given that A has 56 subsets more than B

\Rightarrow 2 ^{m}-2 ^{n}=56

Taking 2 ^{n} as common;

 2^{n}(2^{m-n}-1)=56

 2^{n}(2^{m-n}-1)=2^{3}(2^{3}-1)

\Rightarrow n=3, m-n=3

\Rightarrow n=3, m=6


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 = = 2 ^{n}-1

Here n is the number of elements in a set

so, number of proper subsets for given set is = 2 ^{3}-1=8-1=7


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}

=> 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. 2 ^{n}

b. 2 ^{n+1}

c.2 ^{n-1}

d. 2 ^{1-n}

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 2 ^{n}

So, it means there will be 2 ^{n} subsets in P(A) or we can say there will be 2 ^{n} 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:

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

Also 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

Who took science =n(S)=70

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

 

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