Let a be a set with 8 elements
a. find the number of subsets of a
b. find the number of subsets of a having one or more elements
c. find the number of subsets of a having exactly one element
d. find the number of subsets of a having two or more elements

a)The number of subsets of A is 256

b)The number of subsets of A having one or more elements is 255

c)The number of subsets of A having exactly one element is 8

d) The number of subsets of A having two or more elements is 247

Step-by-step explanation:

Let A be the set of 8 elements

Formula of number of subsets =

where n is the number of elements

Substitute n = 8

a) So, Number of subsets of A =

                                               =

b)The number of subsets of A having one or more elements

Since the subsets contains ∅ also

So, we will exclude the null set

So, the number of subsets of A having one or more elements = Total no. of subsets - 1

                                                                                                       =256-1

                                                                                                       =255

c)The number of subsets of A having exactly one element

Since the no. of elements are 8 in Set A

So, The number of subsets of A having exactly one element = 8

d. The number of subsets of A having two or more elements

Since The number of subsets of A having exactly one element = 8

The subsets contains ∅ also

So, we will exclude null set and subsets of A having exactly one element

So, The number of subsets of A having two or more elements = 256-(8+1)

                                                                                                       =247

Hence ,

a)The number of subsets of A is 256

b)The number of subsets of A having one or more elements is 255

c)The number of subsets of A having exactly one element is 8

d) The number of subsets of A having two or more elements is 247