Question

Two finite sets have m and n elements . The total no. of subsets of the first set is 56 more than the total no.of subsets in the second set. Find the value of m and n .

Answer 1

let A and B be two sets having m and n numbers of elements respectively
number of subsets of A=2m
number of subsets of B=2n
according to question
2^m-2^n=56
\[2^n (2^{m-n} \ -1)=23(23-1) \]
\[\therefore \]
\[n=3 \ and \ m-n=3\]
\[m=6 \]

Answer 2

Can you get it now!

Answer 3

yea .. but can you explain how in 2^n ( 2^m-n - 1) came ?
like i know taking 2^n common but why 2^m-n inside ?

Answer 4

so that it gets cancelled ?

Answer 5

@IllasMcKay there ?

Answer 6

ya!

Answer 7

okay .. ty for the help :)