Explanation Given information: Let A be the set of all strings of 0’s, 1’s and 2’s of length 4. Define a relation R on A as follows: For all s, t ∈ A, s R t ⇔ the sum of the characters in s equals the sum of the characters in t. Calculation: Reflexive: Since the relation is based on the sum of characters in a string, s = s, so s A s . Thus, reflexive Symmetric: Suppose s and t are strings. If s A t , then s and t have the same sum of their characters, so t A s

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Chapter 8.2, Problem 26ES

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To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

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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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To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Solution Summary: The author explains that the relation R is reflexive, symmetric, transitive or none of these.

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To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

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Chapter 8 Solutions