First slide

Relations XII

Question

Let A and B be two sets containing 2 elements respectively. The number of subsets of A x B having 3 or more elements is

Easy

Solution

$\begin{aligned} (3) n (A \times B) = 2 \times 4 = 8 \\ ^{8} C_{3} +^{8} C_{4} + \dots . . +^{8} C_{8} = 2^{8} - [^{8} C_{0} +^{8} C_{1} +^{8} C_{2}] \\ = 256 - (1 + 8 + 28) = 256 - 37 = 219 \end{aligned}$

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