Ex 1.1
You are here
Last updated at Dec. 16, 2024 by Teachoo
Something went wrong!
The
video
couldn't load due to a technical hiccup.
But don't worry — our team is already on it, and we're working hard to get it back up ASAP.
Thanks for bearing with us!
Transcript
Ex 1.1, 10 Given an example of a relation. Which is (ii) Transitive but neither reflexive nor symmetric. Let R = {(a, b): a < b} Check reflexive Since a cannot be less than a a ≮ a So, (a, a) ∉ R ∴ R is not reflexive. Check symmetric If a < b , then b cannot be less than a i.e. b ≮ a So, if (a, b) ∈ R , (b, a) ∉ R ∴ R is not symmetric Check transitive If a < b & b < c, then a < c So, if (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R ∴ R is transitive. Hence, relation R is transitive but not reflexive and symmetric.
