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

`R = {(a, b) : a, b ∈ N` and `a = b^2}`


(i) It can be seen that `2 in N`; however,` 2 ≠ 2^2 = 4`


Therefore, the statement “(a, a) in R, for all `a in N`” is not true.


(ii) It can be seen that `(9, 3) in N `because` 9, 3 in N` and `9 = 3^2`.


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