Q.4 Show that the relation R in R defined as R = \{(a, b) : a \leq b\}, is reflexive and
transitive but not symmetric.

Answers (1)

R = \{(a, b) : a \leq b\}

As \left ( a,a \right )\in R so it is reflexive.

Now we take an  example 

                                       \left ( 2,3 \right )\in R    as 2< 3

But \left ( 3,2 \right )\notin R  because 2 \nless 3.

So,it is not symmetric.

Now if we take,\left ( 2,3 \right )\in R\, \, and\, \, \left ( 3,4 \right )\in R

Than, \left ( 2,4 \right )\in R because 2< 4

So, it is transitive.

Hence, we can say that it is reflexive and transitive but not symmetric.

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