(a) Why is A A for every set A? (b) Given sets A and B, explain why A B is equiv
ID: 3168265 • Letter: #
Question
(a) Why is A A for every set A? (b) Given sets A and B, explain why A B is equivalent to asserting B A. (c) For three sets A,B, and C, show that A B and B C implies A C. These three properties are what is meant by saying that is an equivalence relation. (a) Why is A A for every set A? (b) Given sets A and B, explain why A B is equivalent to asserting B A. (c) For three sets A,B, and C, show that A B and B C implies A C. These three properties are what is meant by saying that is an equivalence relation. (a) Why is A A for every set A? (b) Given sets A and B, explain why A B is equivalent to asserting B A. (c) For three sets A,B, and C, show that A B and B C implies A C. These three properties are what is meant by saying that is an equivalence relation.Explanation / Answer
a)
~ because in an equivalence relation we havereflexive property ie for an element A
A~A
b)
This is due to the symmetry property of equivalence relation ie A~B implies B~A and vice versa
c)
This is the transitive property of equivalence relations
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