Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than that of the total no. of subsets of the second set. Find the values of m and n.
We have m elements in the first set.
When forming the subset each element has choices; to either get selected or not.
So, each of these m elements has 2 choices.
Therefore, total possible selections from first set = 2m
Similarly, total possible selections from second set = 2n
Hence, 2m – 2n = 56
This is only true when 64 – 8 = 56.
or 26 – 23 = 56
Therefore m = 6 and n = 3