Let R = {(1, 2), (3, 4), (2, 2)} and S = {(4, 2), (2, 5), (3, 1), (1, 3)} be two relations. The composite relation R∘S of R and S is :
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Correct answer: B. (1, 5), (3, 2), (2, 5)
Explanation
Using R∘S = {(a, c) : there exists b with (a, b) ∈ R and (b, c) ∈ S}, i.e. applying R first and then S: from (1, 2) ∈ R and (2, 5) ∈ S we get (1, 5); from (3, 4) ∈ R and (4, 2) ∈ S we get (3, 2); from (2, 2) ∈ R and (2, 5) ∈ S we get (2, 5). Combining these pairs gives R∘S = {(1, 5), (3, 2), (2, 5)}.More Discrete Structures and Optimisation questions
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