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Determine whether the relation R defined on the set R of all real numbers as R = {(a, b) ; a, b ϵ R and a-b + √3ϵ S, where S is the set of all irrational numbers}, is reflexive, symmetric and transitive. OR Let A = R×R and ∗ be the binary operation on A defined by (a,b) ∗ (c, d) - (a + c, b + d). Prove that ∗ is commutative and associative. Find the identity element for ∗ on A. Also write the inverse element of the element (3, -5) in A. |
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Answer» Determine whether the relation R defined on the set R of all real numbers as R = {(a, b) ; a, b ϵ R and a-b + √3ϵ S, where S is the set of all irrational numbers}, is reflexive, symmetric and transitive. OR Let A = R×R and ∗ be the binary operation on A defined by (a,b) ∗ (c, d) - (a + c, b + d). Prove that ∗ is commutative and associative. Find the identity element for ∗ on A. Also write the inverse element of the element (3, -5) in A. |
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