Question

Set A has two elements and set B has 4 elements then number of subsets of (A X B) having three or more elements are

Answer 1

Given: n(A) = 2, n(B) = 4

So, n(A × B) = n(A) × n(B) = 2 × 4 = 8

Now total number of subset of A × B = 28 = 256

Out of these subset containing zero element = ⁸C₀ = 1

subsets containing one element = ⁸C₁ = 8

subsets containing two elements = ⁸C₂ = 28

So, Subsets having three or more elements = total number of subsets - subsets having less than three elements

= 256 - (1 + 8 + 28) = 256 - 37 = 219