) The domain is a group of people. Person x is related to person y under relation S if x is currently the spouse of person y. You can assume that there is no polygamy and that there is at least one person who is married to another person in the group.   b.) The domain is the set of all integers. xEy if x + y is even. An integer z is even if z = 2k for some integer k.

Q: Let A = {1, 2, 3, 4, 5, 6} and let S = P (A), 1 set of A. the power a. For a, b e S, define a ~ b if…

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Q: Let T be an irreflexive relation on the set M, then the ToT relation is also irreflexive on the set…

A: Let M=ℕ. Define relation T on M as, T=a,b : a≠ b Clearly a,a∉T for any a∈M. Hence T is irreflexive.

Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: d. Ris a relation on Z* such that (x, y) e R if and only if there is a positive integer n such that…

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Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: Consider the following relation on set B = {a, b, {a}, {b}, {a, b}}: P = {(a, b), (b, {a, b}), ({a,…

A: Given that, The set B is: B=a, b, a, b, a, b And, the set P is: P=a, b, b, a, b, a, b, a, b, a, a, a

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

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Q: Give an example of two equivalence relations R and S on

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Q: c. Ris a relation on Z such that (x, y) e R if and only if xy 2 0. d. Ris a relation on Z* such that…

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Q: 4. Let A = {a, b, c, d}. Suppose R is an equivalence relation on A. Suppose R has three equivalence…

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Q: Let A = {x: x is a course offered by Trinity University of Asia} B = {x: x is a college in Trinity…

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Q: S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and…

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Q: Subject: Set Theory

A: To show that Rπ is an equivalence relation on A.The relation Rπ is defined as follows:

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

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Q: Considering A as a set which contains the elements (2,3,4,5,6,7.8}, Define a relation R from A A by…

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Q: Determine whether each relation is an equivalence relation. Justify your answer. If the relation is…

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Q: Broadly speaking, what is a mathematical closure? O A. Only relations have closures. They are…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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Q: Subject: Set Theory

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A: Introduction :

Q: Let A = {a, b, c, d, e}. Suppose R is an equivalence relation on A. Suppose R has two equivalence…

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