# Show that the relation R in the set R of real numbers, defined asR = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.

It is given that R = {(a, b) : a ≤ b2}

Check for reflexive:

We can see that

Since,

Therefore, R is not reflexive.

Check for symmetric:

Now, (1,4) ϵ R as 1 < 42

But 4 is not less than 12.

Then, (4,1) R

Therefore, R is not symmetric.

Check for transitive:

Now, (3, 2), (2, 1.5) ϵ R

But, 3 > (1.5)2 = 2.25.

Then, (3, 1.5) R

Therefore, R is not transitive.

Therefore, R is neither reflexive, nor symmetric, nor transitive.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 0152 mins
Different kind of mappings58 mins
Range of Functions58 mins
Quick Revision of Types of Relations59 mins
Some standard real functions61 mins
Battle of Graphs | various functions & their Graphs48 mins
Functions - 0947 mins
Quick Recap lecture of important graphs & functions58 mins