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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.

Advanced Engineering Mathematics
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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Let A = {1,2,3,4}. For any function ƒ from A to A and any relation R on A, we define a relation S on A by: For all a, b = A, aSbf(a) Rf (b). Prove or disprove each of the following statements. f(a)Rf(b). (a) For every function f 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 ƒ 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.
Transcribed Image Text:Let A = {1,2,3,4}. For any function ƒ from A to A and any relation R on A, we define a relation S on A by: For all a, b = A, aSbf(a) Rf (b). Prove or disprove each of the following statements. f(a)Rf(b). (a) For every function f 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 ƒ 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.
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