Let A=\{-3,-2,-1,0,1,2,3\} and B=\{0,1,4,9\}. How many elements does the subset of A \times B corresponding to the relation R=\{(x,y):|x| \lt y\} have, where x \in A and y \in B?

Explanation

Evaluate the condition |x| \lt y for each y \in B. For y=0, |x| \lt 0 yields no solutions. For y=1, |x| \lt 1 \implies x=0 (1 element). For y=4, |x| \lt 4 \implies x \in A (7 elements). For y=9, |x| \lt 9 \implies x \in A (7 elements). Total elements in the subset = 1 + 7 + 7 = 15.

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