Question

If A and B two sets containing 2 elements and 4 elements, respectively. Then, the number of subsets of `A xx B` having 3 or more elements, is
A. 220
B. 219
C. 211
D. 256

Answer 1

Correct Answer - B
`because A xx B` has 8 elements.
`therefore` Number of subsets = `2^(8) = 256`
Number of subsets with zero element = `.^(8)C_(0) = 1`
Number of subsets with one element = `.^(8)C_(1) = 8`
Number of subsets with one elements = `.^(8)C_(2) = 28`
Hence, Number of subsets of `AxxB` having 3 or more elements
`=256-(1+8+28)=256-37=219`