Two finite sets have m and n elements. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Find the values of m and n.

Asked by Topperlearning User | 17th Apr, 2014, 10:00: AM

Expert Answer:

                G i v e n :
space space space space space 2 to the power of m minus 2 to the power of n equals 112

rightwards double arrow 2 to the power of n open parentheses 2 to the power of m minus n end exponent minus 1 close parentheses equals 112

rightwards double arrow 2 to the power of n open parentheses 2 to the power of m minus n end exponent minus 1 close parentheses equals 2 to the power of 4 cross times 7 equals 2 to the power of 4 open parentheses 2 cubed minus 1 close parentheses

rightwards double arrow n equals 4 space a n d space m minus n equals 3

rightwards double arrow m equals 7

Answered by  | 17th Apr, 2014, 12:00: PM