Question

The number of elements of the power sets of sets X & Y are 32 & 64. The number of elements of the power set of (X∪Y) is 512.

Find the number of elements in the power set of (X∩Y). reply ASAP! :)

Answer 1

Number of elements in the power set of X = 32 = 2⁵

So, number of elements in X = 5

Number of elements in the power set of Y = 64 = 2⁶

So, number of elements in Y = 6

Number of elements in X∩Y, i.e elements common to both X and Y = Number of elements in the smaller set = Number of elements in X = 5

Hence, the number of elements in the power set of X∩Y = 2⁵ = 32