Explanation Given information: Let R be the relation on a set A, the set of all ordered pairs of integers for which the second element of the pair is nonzero. Define a relation R on A as follows: For all ( a , b ) , ( c , d ) ∈ A , ( a , b ) R ( c , d ) ⇔ a d = b c Proof: A = Z × ( Z − { 0 } ) R = { ( ( a , b ) , ( To determine (b) To prove that R is symmetric.. To determine (c) To list four distinct elements in [(1, 3)]. To determine (d) To list four distinct elements in [(2, 5)].

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ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 8.3, Problem 42ES

To determine

(a)

To prove that R is reflexive.

To determine

(b)

To prove that R is symmetric..

To determine

(c)

To list four distinct elements in [(1, 3)].

To determine

(d)

To list four distinct elements in [(2, 5)].

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Chapter 8.3, Problem 41ES

Chapter 8.3, Problem 43ES

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Chapter 8 Solutions

Discrete Mathematics With Applications

Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - Prob. 2TY Ch. 8.1 - Prob. 3TY Ch. 8.1 - Prob. 4TY Ch. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Prob. 5ES

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(a) To prove that R is reflexive.

Solution Summary: The author explains that R is reflexive by using the commutative property of multiplication.

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(a) To prove that R is reflexive.

(b) To prove that R is symmetric..

(c) To list four distinct elements in [(1, 3)].

(d) To list four distinct elements in [(2, 5)].

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Chapter 8 Solutions

(a)

To prove that R is reflexive.

(b)

To prove that R is symmetric..

(c)

To list four distinct elements in [(1, 3)].

(d)

To list four distinct elements in [(2, 5)].