If the mappings f and g are given by f={(1, 2),(3, 5),(4,1)},g={(2, 3),(5, 1),(1, 3)}, then write down pairs in the mappings $g o f$ (3).

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Solution

If $f ϵ X \times Y$ and $g ϵ Y \times Z$
Then
$g o f ϵ X \times Z$ i.e
$(x, z) ϵ g o f$
Therefore
$g o f = {(1, 2) | (2, 3), (3, 5) | (5, 1), (4, 1) | (1, 3)}$
$= {(1, 3), (3, 1), (4, 3)}$
Hence
$g o f (3) = 1$

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