Let R be a relation from Q to Q defined by R={(a, b): a, b ∈ Q and a-b ∈ Z } . Show that (a, b)

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2.Relations and Functions

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Let $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that

$(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$

Option A

Option B

Option C

Option D

Solution

$(a, b)$ and $(b, c) \in R$ implies that $a-b \in Z . b-c \in Z .$ So, $a-c=(a-b)+(b-c) \in Z .$ Therefore, $(a, c) \in R$

Standard 11

Mathematics

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