In each item below, verify that ~ is an equivalence relation on the given set. (a) Let S = Z x N. Define the relation - on S as: (a, b) ~ (c, d) if and only if ad – bc = 0. Moreover, if a and b are relatively prime, how are c and d related to a and b?

Q: Suppose R is a relation defined on the set A = {1,2, 3, 4}. If R is an equivalence relation, what is…

A: Given below the detailed solution

Q: , In each item below, verify that - is an equivalence relation on the given set. (b) Let - be a…

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Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

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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: In the following questions, determine whether the binary relation is: (1) reflexive, (2) symmetric,…

A: Note: Sorry. We can't provide a handwritten solution. Since there is no part a for the given…

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Q: for an equivalence relation R on A, both sets, the class of equivalence classes of R —A/R— is a set.

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Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…

A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…

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A: partial order means reflexive and antisymmetric.

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Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

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A: (a)

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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.

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A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

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Q: 14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an…

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Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

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A: Let A is the set of all students at your college. For every x,y∈A,  xSy⇔x is the same age as y. That…