Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric

Answer
Method - 1 
R = {(a, b); a ≤ b}
Clearly (a, a) ∈ R as a = a.
∴R is reflexive.
Now,
(2, 4) ∈ R (as 2 < 4) But, (4, 2) ∉ R as 4 is greater than 2.
∴ R is not symmetric.
Now, let (a, b), (b, c) ∈ R.
Then, a ≤ b and b ≤ c

⇒ a ≤ c
⇒ (a, c) ∈ R ∴R is transitive.
Hence,R is reflexive and transitive but not symmetric.
Method - 2

Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.

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