First slide

Introduction to Relations (XI) on Sets

Question

If two sets A and B are having 99 elements in common the number of elements common to each of the sets AxB and Bx A are $121 λ^{2}$ the value of $λ$ is

Easy

Solution

$\begin{aligned} n ((A \times B) \cap (B \times A)) & = n ((A \cap B) \times (B \cap A)) \\ = n (A \cap B) \cdot n (B \cap A) \\ = n (A \cap B) \cdot n (A \cap B) \\ = 99 \times 99 = 121 \times 9^{2} \\ ∴ λ & = 9 \end{aligned}$

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