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Show that the relation R in the set R of Real numbers defined as R = {(a, b): a ≤ b2} is neither reflexive, nor symmetric nor transitive. |
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Answer» a ≤ a2 is not true for all a. So (a, a) ∉ R hence not Reflexive. (a, b) ∈ R ⇒ a ≤ b2 does not imply that b ≤ a2. So (b, a) ∉ R, hence not Symmetric. (a, b),(b, c) ∈ R ⇒ a ≤ b2 and b ≤ c2 does not imply that a ≤ c2. So (a, c) ∉ R, hence not Transitive. |
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