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Question
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
Solution
We are given ,
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
\[\because a + b = b + \text{ a for all a, b } \in N\]
\[ \therefore (a, b) R (a, b) \text{ for all a, b } \in N\]
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