Question

2. The total number of subsets of a
finite set A has 56 more elements
than the total number of subsets of
another finite set B. What is the
number of elements in the set A?
(a) 5
(6) 6
(c) 7
(d) 8​

Answer 1

5

6

7

8

Answer :

B

Solution :

Let set A and B have m and n elements respectively. The set made by subsets of a finite set A and B is known as power set i.e. P(A) and P(B).

We know, if set A has n elements then P(A) has 2n elements.

Thus, The total no. of subsets of a finite set A=2m and set B=2n

So, According to the question

2m−2n=56

⇒2n(2m−n−1)=8×7=23×(23−1)

On comparing the power, both side

n=3 and m-n=3

implies m=6 and n=3