If A = (a, b, c, d), B= (p, q, r, s). then which of the following are relations from A to B? Give reasons for your answer:

R_{1}

= {( a, p), (b, r), (c, s)}

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R_{2}

= { ( q, b), (c, s), (d, r)}

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R_{3}

= {(a, p), (a, q), (d, p), (c, r), (b, r)}

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R_{4}

= {(a, p), (a, q), (b, s), (s, b)}

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Solution

The correct options are
A $R_{1}$ = {( a, p), (b, r), (c, s)}
C $R_{3}$ = {(a, p), (a, q), (d, p), (c, r), (b, r)}
(A) .(C)
If R is a relation from A to B, then R $\subset (A \times B)$ which consists of all ordered pairs of the type. (x, y) such that $x \in A, y \in B$ .
Clearly, $R_{1}$ and $R_{3}$ are such sets of $A \times B$ . The elements (q, b), of $R_{2} \in (B \times A)$ and not $A \times B$ and the elements (q, b), and (s, b), of $R_{4}$ also not belong to $A \times B$ and as such $R_{2}$ and $R_{4}$ are not relations from A to B.

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