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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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The correct Answer is:
N/a
`R={(a,b):a,b inN and a=b^(2)}`
(i) For each a `in` N, (a,a) `in` R is false
If a=2 then `(2,2)in R " "implies" "2ne2^(2)`
(ii) Let a, b `in` N and (a,b) `in` R
`{:(implies,a=b^(2),implies,bnea^(2)),(implies,(b","a)neR,,):}`
Therefore given statement is false.
(iii) Let a,b,c `in` N
`and(a,b)inRand (b,c)inR`
`{:(implies,a=b^(2),and,b=c^(2)),(implies,a=(c^(2))^(2),implies,a=c^(4)),(implies,anec^(2),implies,(a,c)notinR):}`
Therefore, given statement is false.
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