Let and be two relations defined as follows: and , where is the set of all rational numbers. Then...

(a) : For Let is not transitive For : Let Then, in Q is not transitive. ...

Let R_{1} and R_{2} be two relations defined as follows: R_{1} = { (a,b) in R^{2}:a^{2} + b^{2} in Q } and R_{2} = { (a,b) in R^{2}:a^{2} + b^{2} notin Q }, where Q is the set of all rational numbers. Then: Relation (Mathematics)

Exam ( $3^{rd\ }$ Sept $2^{nd\ }$ Shift 2020)

Mathematics

Let

R_{1}

and

R_{2}

be two relations defined as follows:

R_{1} = \left\{ (a,b) \in R^{2}:a^{2} + b^{2} \in Q \right\}

and

R_{2} = \left\{ (a,b) \in R^{2}:a^{2} + b^{2} \notin Q \right\}

, where

Q

is the set of all rational numbers. Then

Neither

R_{1}

nor

R_{2}

is transitive.

R_{2}

is transitive but

R_{1}

is not transitive.

R_{1}

is transitive but

R_{2}

is not transitive.

R_{1}

and

R_{2}

are both transitive.

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