Question

show that the relation R on R defined as R={(a,b);a<b2} is neither reflexive nor symmetric nor transitive​

Answer 1

Answer:

R = {(a, b): a ≤ b2}

It can be observed that 

(12,12)∉R,since12>(12)2=14

∴R is not reflexive.

Now, (1, 4) ∈ R as 1 < 42

But, 4 is not less than 12.

∴(4, 1) ∉ R

∴R is not symmetric.

Now,

(3, 2), (2, 1.5) ∈ R

(as 3 < 22 = 4 and 2 < (1.5)2 = 2.25)

But, 3 > (1.5)2 = 2.25

∴(3, 1.5) ∉ R

∴ R is not transitive.

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

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