# Q9 (3)  Let R be a relation from N to N defined by $R = \left \{ ( a,b): a,b \epsilon N \: \:and \: \: a = b ^ 2 \right \}$ . Are             the following true?       (a,b) $\epsilon$ R, (b,c) $\epsilon$ R implies (a,c) $\epsilon$ R.

G Gautam harsolia

It is given that
$R = \left \{ ( a,b): a,b \epsilon N \: \:and \: \: a = b ^ 2 \right \}$
And
$( a,b ) \ \epsilon \ R , (b,c) \ \epsilon \ R$ implies $(a,c) \ \epsilon \ R$
Now, it can be seen that  $(16,4) \ \epsilon \ R , ( 4,2 ) \ \epsilon \ R$  because  $16 = 4^2 = 16$  and $4 = 2^2 = 4$ ,  But  $16 \neq 2^2 =4$
Therefore,  $(16,2) \ \notin \ N$
Therefore, the given statement is FALSE

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