Let A = {1, 2, 3, 4}. For any function f from A to A and any relation R on A, we define a relation S on A by: For all a, bЄ A, aSb f(a) Rf(b). Prove or disprove each of the following statements. (a) For every function ƒ from A to A and every relation R on A, if R is reflexive, then S is reflexive. (b) For every function f from A to A and every relation R on A, if S is reflexive, then R is reflexive. (c) For every function f from A to A and every relation R on A, if R is symmetric, then S is symmetric. (d) For every function f from A to A and every relation R on A, if S is symmetric, then R is symmetric.

Let A = {1, 2, 3, 4}. For any function f from A to A and any relation R on A, we define a relation S on A by: For all a, bЄ A, aSb f(a) Rf(b). Prove or disprove each of the following statements. (a) For every function ƒ from A to A and every relation R on A, if R is reflexive, then S is reflexive. (b) For every function f from A to A and every relation R on A, if S is reflexive, then R is reflexive. (c) For every function f from A to A and every relation R on A, if R is symmetric, then S is symmetric. (d) For every function f from A to A and every relation R on A, if S is symmetric, then R is symmetric.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 63E

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