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 $(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$.
(N/A) Given that $(a, b) \in R$,it implies $a - b \in Z$.
Given that $(b, c) \in R$,it implies $b - c \in Z$.
We need to check if $(a, c) \in R$,which requires $a - c \in Z$.
Consider $a - c = (a - b) + (b - c)$.
Since the sum of two integers is always an integer,$(a - b) + (b - c) \in Z$.
Therefore,$a - c \in Z$,which implies $(a, c) \in R$.
Given that $(b, c) \in R$,it implies $b - c \in Z$.
We need to check if $(a, c) \in R$,which requires $a - c \in Z$.
Consider $a - c = (a - b) + (b - c)$.
Since the sum of two integers is always an integer,$(a - b) + (b - c) \in Z$.
Therefore,$a - c \in Z$,which implies $(a, c) \in R$.
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