Let $R$ be a relation from $Q$ to $Q$ defined by $R = \{(a, b) : a, b \in Q \text{ and } a - b \in Z \}$. Show that $(a, a) \in R$ for all $a \in Q$.
(N/A) To show that $(a, a) \in R$ for all $a \in Q$,we check the definition of the relation $R$.
By definition,$(a, b) \in R$ if $a - b \in Z$.
For the pair $(a, a)$,we have $a - a = 0$.
Since $0$ is an integer $(0 \in Z)$,it follows that $(a, a) \in R$ for all $a \in Q$.
By definition,$(a, b) \in R$ if $a - b \in Z$.
For the pair $(a, a)$,we have $a - a = 0$.
Since $0$ is an integer $(0 \in Z)$,it follows that $(a, a) \in R$ for all $a \in Q$.
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