Let R be a relation from N to N defined by R = `{(a,b) in N and a = b^2}`. Are the following true? `{(a,a) in R`, for all `a in N`}

Explanation

i) No. `[(a, a) in N` only for `(1,1)` and `(0,0)]`

ii) No. `[a, b in N rarr(a, b) in N` only for `(1,1)` and `(0,0)]`

iii) No. `[a=c^2 rarr b^2=c^2 rarr b=c.`

`therefore(a, b) in N` and `(b, c) in N rarr(a, c) in N` if `b=c mid`