Discrete Mathematics with Graph Theory (3rd Edition) 45

Discrete Mathematics with Graph Theory (3rd Edition) 45 -...

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Section 2.4 43 13. (a) [BB] Yes, this is an equivalence relation. Reflexive: Note that if a is any triangle, a '" a because a is congruent to itself. Symmetric: Assume a '" b. Then a and b are congruent. Therefore, b and a are congruent, so b", a. Transitive: If a '" b and b '" c, then a and b are congruent and b and c are congruent, so a and c are congruent. Thus, a '" c. (b) Yes, this is an equivalence relation. Reflexive: If a is a circle, then a '" a because a has the same center as itself. Symmetric: Assume a '" b. Then a and b have the same center. Thus, b and a have the same center, so b '" a. Transitive: Assume a '" b and b '" c. Then a and b have the same center and b and c have the same center, so a and c have the same center. Thus, a '" c. (c) Yes, this is an equivalence relation. Reflexive: If a is a line, then a is parallel to itself, so a '" a. Symmetric: If a '" b, then a is parallel to b. Thus, b is parallel to a. Hence, b '" a. Transitive:
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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