Let A, B, and C be sets. Prove or disprove: If R and S are equivalence relations on A, then S o R is an equivalence relation on A. Justify your answer.
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A: According to question given that Set Z in which the relation R is defined by aRbIf and only if a+3b…
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A: We will answer the first question as you didn't specify any. Please resubmit the other question…
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A: Introduction :
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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
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Q: 1. Let X be a set, R, S C X × X binary relations on X. Prove or disprove the following. (a) If R and…
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- True or False Label each of the following statements as either true or false. Let be an equivalence relation on a nonempty setand let and be in. If, then.Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
- Label each of the following statements as either true or false. If R is an equivalence relation on a nonempty set A, then any two equivalence classes of R contain the same number of element.Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in each case whether R is an equivalence relation, and justify your answers. (a,b)R(c,d) if and only if ad=bc. (a,b)R(c,d) if and only if ab=cd. (a,b)R(c,d) if and only if a2+b2=c2+d2. (a,b)R(c,d) if and only if ab=cd.