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 ,

Explanation

To determine the truth of the statements regarding the relation \( R = \{(a, b) : a = b^2 \} \) where \( a, b \in \mathbb{N} \), we will analyze each statement step by step.

### Step 1: Analyze statement (i)
**Statement (i):** \( (a, a) \in R \) for all \( a \in \mathbb{N} \).

**Solution:**
For \( (a, a) \) to be in \( R \), it must satisfy the condition \( a = b^2 \). Here, we set \( b = a \). Therefore, we need to check if \( a = a^2 \).

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