CBSE Class 12-science Answered
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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