Class 12 Mathematics - Chapter Relations and Functions NCERT Solutions | Show that the relation R in R defined as
Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive but not symmetric.
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.
More Questions From Class 12 Mathematics - Chapter Relations and Functions
- Q:- Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.
(ii) Transitive but neither reflexive nor symmetric.
(iii) Reflexive and symmetric but not transitive.
(iv) Reflexive and transitive but not symmetric.
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(ii) Relation R in the set N of natural numbers defined as
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(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
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(C) f is one-one but not onto
(D) f is neither one-one nor onto.
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