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?

$(a, b) \in R,$ implies $(b, a) \in R$

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 $(9,3)$ $\in N$ because $9,3 \in N$ and $9=3^{2} .$ Now, $3 \neq 9^{2}=81$ $(3,9)$ $\notin N$

Therefore, the statement $"(a, b) \in R,$ implies $"(b, a) \in R "$ is not true.

Standard 11

Mathematics

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