Prove that the relation R on a set A is symmetric if and only if R = R^−1 , where R^−1 is the inverse relation of R. b) Prove that the relation R on a set A is antisymmetric if and only if R ∩ R^−1 is subset of the relation ∆= {(a, a) | a ∈ A}

Prove that the relation R on a set A is symmetric if and only if R = R^−1 , where R^−1 is the inverse relation of R. b) Prove that the relation R on a set A is antisymmetric if and only if R ∩ R^−1 is subset of the relation ∆= {(a, a) | a ∈ A}

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a) Prove that the relation R on a set A is symmetric if and only if R = R^−1 , where R^−1 is the inverse relation of R. b) Prove that the relation R on a set A is antisymmetric if and only if R ∩ R^−1 is subset of the relation ∆= {(a, a) | a ∈ A}

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