Given two sets $A = {a, b, c} & B = {1, 2, 3} .$
If $R = {(a, 2), (a, 3), (b, 1), (c, 3), (b, 2)}$
$& S = {(a, 3), (b, 1), (c, 2), (2, a)} .$ Then select the correct statement.

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Solution

Given: $A = {a, b, c}$ and $B = {1, 2, 3}$

$\Rightarrow A \times B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3), (c, 1), (c, 2), (c, 3)}$

$(i) R = {(a, 2), (a, 3), (b, 1), (c, 3), (b, 2)}$
It can be seen easily, for all $(x, y) \in R$
$\Rightarrow (x, y) \in A \times B$
$∴ R \subseteq A \times B$
Hence, $R$ is a relation from $A t o B$

$(i i) S = {(a, 3), (b, 1), (c, 2), (2, a)}$
Here $(2, a) \in S but (2, a) \notin A \times B$
So, $S \subset̸ A \times B$
$∴ S$ is not a relation from $A t o B$
Hence, $R$ is a relation but $S$ is not from $A t o B$

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