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show that the relation R on R defined as R={(a,b):a<_b } is reflexive, transitive but not symmetric Chapter: Relations and functions
Asked by niharikapabba2605 | 12 Oct, 2018, 12:43: PM Expert Answer

R = {(a, b); a ≤ b}

Obviously, (a, a) ∈ R as a = a.

Hence, R is reflexive.

Now,

(1, 2) ∈ R (as 1 < 2)

But, (2, 1) ∉ R as 2 is greater than 1.

Hence, R is not symmetric.

Let (a, b), (b, c) ∈ R.

Then,

a ≤ b and b ≤ c

⇒ a ≤ c

⇒ (a, c) ∈ R

Hence, R is transitive.

Hence, R is reflexive and transitive but not symmetric.

Answered by Sneha shidid | 15 Oct, 2018, 09:51: AM
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