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Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!. (c) If SC R, then S-1 C R-!.

Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!. (c) If SC R, then S-1 C R-!.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...
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Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-)- = R. (b) (RU S)-1 = R-'Us-I. (c) If SC R, then S-' C R-!.
Transcribed Image Text:Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-)- = R. (b) (RU S)-1 = R-'Us-I. (c) If SC R, then S-' C R-!.
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