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  • Let R be a relation from N to N defined by R = {(a, b) : a, b belongs to N and a = b^ 2 }. Are the following true?

Q9 (2)  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,a ) \epsilon R , implies (b,a)  \epsilon R

Answers (1)

best_answer

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

Posted by

Gautam harsolia

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