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Question
Let us define a relation R in R as aRb if a ≥ b. Then R is ______.
Options
An equivalence relation
Reflexive, transitive but not symmetric
Symmetric, transitive but not reflexive
Neither transitive nor reflexive but symmetric
Solution
Let us define a relation R in R as aRb if a ≥ b. Then R is reflexive, transitive but not symmetric.
Explanation:
Given that, aRb if a ≥ b
⇒ aRa
⇒ a ≥ a which is true.
Let aRb, a ≥ b, then b ≥ a which i not true,
So R is not symmetric.
But aRb and bRc
⇒ a ≥ b and b ≥ c
⇒ a ≥ c
Hence, R is transitive.
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