Let R be a relation from N to N defined by R =left{(a, b): a, b ∈ N text { and } a=b^{2}right} . A

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2.Relations and Functions

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Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?

$(a, a) \in R ,$ for all $a \in N$

Option A

Option B

Option C

Option D

Solution

$R=\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\}$

It can be seen that $2 \in N$; however, $2 \neq 2^{2}=4$

Therefore, the statement $''(a, a) \in R,$ for all $a \in N ^{\prime \prime}$ is not true.

Standard 11

Mathematics

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