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Let R be a relation from N to N defined...

Let R be a relation from N to N defined by `R = {(a , b) : adot b in N`and `a=b^2`). Are the following true?(i) `(a , a) in R , for a l l a in N`(ii) `(a , b) in R , i m p l i e s (b , a) in R`(iii) `(a ,

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To solve the problem, we need to analyze the relation \( R \) defined by \( R = \{(a, b) : a, b \in \mathbb{N} \text{ and } a = b^2\} \) and check the validity of the three statements provided. ### Step-by-step Solution: **Statement (i):** \( (a, a) \in R \) for all \( a \in \mathbb{N} \). 1. For \( (a, a) \) to be in \( R \), it must satisfy the condition \( a = b^2 \) where \( b = a \). 2. This means we need to check if \( a = a^2 \). ...
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