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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 (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.

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 , (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
 

Posted by

Gautam harsolia

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