Question

(ii) If B C A and if B has one element less than that
of A, prove that A has twice as many subsets as B.
(iii) Deduce from these two results that a set with 2
elements has 22 subsets, a set with 3 elements
has 23 subsets ; and so on.
How many subsets does a set with n elements
have ?​

Answer 1

Step-by-step explanation:

(i). Given: B is subset of A. B has one element less than A

let number of elements in A = n

then number of elements in B = n-1

formula for number of subsets = 2^number of elements

then number of subsets of A = 2^n

number of subsets of B = 2^(n-1) = 2^n/2

so number of subsets of B = number of subsets of A/2

number of subsets of A = 2 * number of subsets of A

therefore, A has twice as many subsets as B.