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Mathematics, 29.02.2020 01:23 pr4ever
1. Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(a, b) | a and b are the same age}. b) {(a, b) | a and b have the same parents}.c) {(a, b) | a and b share a common parent}.d) {(a, b) | a and b have met}.e) {(a, b) | a and b speak a common language}. 2. Find equivalence classes of following relations if they exist. a) {(0, 0), (1, 1), (2, 2), (3, 3).b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)}.c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)}.d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}.e) {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 2), (3, 3)}.
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