Question

if the number of subsets of A is 56 more than the number of subsets of B ,then find m and n​

Answer 1

Given, The number of subsets of A is 56 more than the number of subsets of B. n(A) = m and n(B) = n .

We need to find the value of m and n.

According to the question,

⇒ 2^(m) - 2^(n) = 56 [ Number of subsets of a set A = 2^(number of elements) ]

⇒ 2^(n) { 2^(m - n) - 1 } = 2³ ( 2³ - 1 )

Here, the bases are same hence the exponent must also be same.

∴ 2^n = 2^3 ⇒ n = 3 ...(1)

Also,

⇒ 2^(m - n) = 2^(3)

⇒ m - 3 = 3 [ from (1) ]

⇒ m = 6

Hence, Value of m is 6 and value of n is 3

Some Information :-

◉ Sets : Set is a collection of data that contains no duplicate values.

Number of subsets : 2^(n)

Where, n = number of elements