Let \( \mathrm{A}=\{1,2,3, \ldots \ldots 9\} \) and \( \mathrm{R} \...

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Let \( \mathrm{A}=\{1,2,3, \ldots \ldots 9\} \) and \( \mathrm{R} \) be the relation in \( \mathrm{A} \times \mathrm{A} \) defined by \( (a, b) \mathrm{R}(c, d) \) if \( a+d=b+c \), for \( (a, b),(c, d) \in \mathrm{A} \times \mathrm{A} \). Prove that \( \mathrm{R} \) is an equivalence relation. Also, obtain the equivalnce class \( [(2,5)] \).
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