# 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= and number of subsets of set B=

It is given that A has 56 subsets more than B

Taking as common;

**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}

=> 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:**

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