SN Dey Class 11 Solutions | SN Dey Class 11 Set Theory Solutions | Class 11 Set Theory MCQ | SN Dey Solutions | S N Dey Math Solutions | Set Theory S N Dey Solutions | WBCHSE Class 11 Math Solutions | Set theory objective questions
SN Dey Class 11 Set Theory MCQ Solutions
Choose the correct option:
Ex 1: The number of subsets in a set consisting of four distinct elements is-
(A) 4 (B) 8 (C) 16 (D) 64
Answer:
We know that the number of subsets in a set consisting of n distinct elements is equal to 2n.
So the answer is
= 24 = 16.
∴ option (C) is correct.
Ex 2: The number of proper subsets in a set consisting of five distinct elements is-
(A) 5 (B) 10 (C) 32 (D) 31
Answer:
We know that the number of proper subsets in a set consisting of n distinct elements is equal to 2n-1.
So the answer is
= 25-1= 32-1 = 31.
∴ option (D) is correct.
Ex 3: If x ∈ A ⇒ x ∈ B then –
(A) A=B (B) A⊂B (C) A⊆B (D) B⊆A
Answer:
As x ∈ A ⇒ x ∈ B, then we must have that either A is a proper subset of B or they are equal. So the answer is A ⊆ B.
∴ option (C) is correct.
Ex 4: If A⊆B and B⊆A then –
(A) A=Φ (B) A∩B=Φ (C) A=B (D) None of these
Answer:
As A⊆B and B⊆A, then it follows that A=B.
So option (C) is correct.
Ex 5: For two sets A and B, if A∪B = A∩B then –
(A) A⊆B (B) B⊆A (C) A=B (D) None of these
Answer:
Let then
As
⇒
…..(i)
Similarly, if then, =
⇒
Thus, we get that B…..(ii)
So from (i) and (ii), we obtain that
∴ option (C) is correct.
Ex 6: A – B = Φ iff – [Council Sample Question ’13]
(A) A≠B (B) A⊂B (C) B⊂A (D) A∩B=Φ
Answer:
We know that A-B ={x: x ∈ A but x ∉B}. Thus A-B=Φ means that A is fully contained in B, that is, A⊂B.
∴ option (B) is correct.
Ex 7: If A∩B = B then –
(A) A⊆B (B) B⊆A (C) A=B (D) A=Φ
Answer:
As B=A∩B, we have B ⊆ A∩B.
⇒ B ⊆ A and B ⊆ B.
⇒ B ⊆ A is true.
∴ option (B) is correct.
Ex 8: If A and B are two disjoint sets then n(A∪B)=
(A) n(A)+n(B) (B) n(A)-n(B) (C) 0 (D) None of these
Answer:
As A and B are disjoint sets, so we have A∩B = Φ. Thus n(A∩B)=0.
Now, we know that
n(A∪B) = n(A)+n(B)-n(A∩B)
= n(A)+n(B)+0
= n(A)+n(B)
∴ option (A) is correct.
Ex 9: For any two sets A and B, n(A)+n(B)-n(A∩B)=
(A) n(A∪B) (B) n(A)-n(B) (C) Φ (D) None of these
Answer:
As n(A∪B) = n(A)+n(B)+n(A∩B), the option (A) is correct.
Ex 10: The dual of A∪U = U is-
(A) A∪U=U (B) A∪Φ=Φ (C) A∪Φ=A (D) A∩Φ=Φ
Answer:
The dual of A∪U = U is A∩Φ=Φ.
∴ option (D) is correct.
Ex 14: State which of the is the set of factors of the number 12-
(A) {2, 3, 4, 6} (B) {2, 3, 4, 6, 12}
(C) {2, 3, 4, 8, 6} (D) {1, 2, 3, 4, 6, 12}
Answer:
The factors of 12 are 1, 2, 3, 4, 6, and 12.
∴ option (D) is correct.
