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  • Let us define a relation R in R as aRb if a ≥ b. Then R is (a) an equivalence relation (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric.

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

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

Answers (1)

(b).

The defined relation R in R as aRb if a \geq b.\\

Similarly, aRa implies a \geq a  which is true. 

Therefore, it is reflexive. 

Let aRb \rightarrow a \geq b, but, b \ngtr a.\\

Therefore, we can’t write it as Rba

Hence, R is not symmetric. 

Now, a \geq b, b \geq c. So, a \geq c,  and this is true. 

Therefore, R is transitive. 

Posted by

infoexpert22

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