Choose the correct answer from the given four options. Let us def… - Vidyadip

Question

Choose the correct answer from the given four options.
Let us define a relation R in R as aRb if a ≥ b. Then R is:

An equivalence relation.
Reflexive, transitive but not symmetric.
Symmetric, transitive but not reflexive.
Neither transitive nor reflexive but symmetric.

✓

Answer

Reflexive, transitive but not symmetric.

Solution:
We are given that, aRb if a ≥ b
⇒ aRa ⇒ a ≥ a which is true.
For relation aRb to be symmetric, we must have a ≥ b and b ≥ a which can’t be possible.
Hence, R is not symmetric.
For relation aRb to be transitive, we must have aRb and bRc.
⇒ a ≥ b and b ≥ c
⇒ a ≥ c
Hence, R is transitive.

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