Two finite sets A and B have 'm' and 'n' elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then find 'm'.
Let A and B be such sets,
i.e, n(A) = m and n(B) = n
[n(A) = no. of elements in set A
n(B) = no. of elements in set B]
n(P(A)) = 2m
n(P(B)) = 2n
[n(P(A)) = no. of elements in Power set of A = no. of subsets of A]
[n(P(B)) = no. of elements in Power set of B = no. of subsets of B]
n(P(A)) - n(P(B)) = 112
i.e, 2m - 2n = 112
2n(2m-n - 1 ) = 24 (7) ------------------- **
From **,
: . 2n = 24
n = 4
From **,
(2m-n - 1 ) = (7)
2m-n = 7 + 1
2m-n = 8
2m-n =23
m - n = 3
subsitituting n =4 ,
m - 4 = 3
m = 7