Question

The number of proper subsets of the set {3, 4, 5, 6, 7} is(a) 32(b) 31(c) 30(d) 25

Answer 1

Let A = { 3,4,5,6,7 }

n( A ) = 5 ,

Number of proper subsets of A

= [2^n(A)] - 1

= [ 2^5 ] - 1

= 32 - 1

= 31

Option ( b ) is correct.

••••

Answer 2

Answer:

(b) 31

Explanation:

A proper subset is defined as a subset of a certain set that is not equal to the set. The subset would contain some elements of the original set but not all the elements

A power set is defined as the set that contains all the subsets of the original set including the set itself. It is calculated as 2ⁿ where "n" is the number of elements in the set.

Now, for the given question:

Set = {3, 4, 5, 6, 7}

Number of elements in the set = 5

Power set = 2ⁿ = 2⁵ = 32

number of proper sets = Power set - 1

Number of proper sets = 32 - 1 = 31 sets

Hope this helps :)