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

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