Relation on $S\times S$

Question

I am having problem in making relations for this question.

$S = \{1, 2, 3, 4\}, A = S \times S; (a,b) R (c,d)$ if and only if $ad = bc$.

I have made the following relations, but I am not sure if these are correct or not.

$R = \{(1,1), (2,2), (3,3), (4,4)\}$.

Please let me know what is the correct answer.

Thanks.

Answer 1

A relation on a set $T$ is a set of ordered pairs of elements of $T$. Your $R$ is a relation on $A$, which is itself a set of ordered pairs, so $R$ is not a set of ordered pairs, but a set of ordered pairs of ordered pairs. It is the set of all things of the form $((a,b),(c,d))$ such that $ad=bc$. One element of $R$ is $((1,2),(2,4))$.