Let us define a relation R in R as aRb if a b . Then, R is

It is given that,, aRb if a b aRa a a which is true. Let aRb, a b , then b a which is not true R is not symmetric. But aRb and bRc a b and b c a c Hence we can say that R is transitive.

Relations and Functions — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp.Q.32,Page 14

Question

Let us define a relation $R$ in $R$ as $aRb$ if $a \ge b$. Then, $R$ is

(a) an equivalence relation
(b) For reflexive, transitive but not symmetric ✓ Correct
(c) For symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric

Step-by-step Solution

It is given that,, $aRb$ if $a \ge b$

$\Rightarrow$ $aRa \Rightarrow a \ge a$ which is true.

Let $aRb,$ $a \ge b$, then $b \ge a$ which is not true $R$ is not symmetric.

But $aRb$ and $bRc$

$\Rightarrow$ $a \ge b$ and $b \ge c$

$\Rightarrow$ $a \ge c$

Hence we can say that $R$ is transitive.

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