Respuesta :
Answer:
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 = [tex]2^n[/tex]
where n is the number of elements
Substitute n = 8
a) So, Number of subsets of A = [tex]2^8[/tex]
= [tex]256[/tex]
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
