Show that the relation R on Z defined by a R b if and only if 5a − 3b is even, for a, b ∈ Z, is an equivalence relation.

Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: Consider the following relation < over reals: x < y iff (x– y) e Z. Prove that it is an equivalence…

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Q: 3. Let R be the relation on the set of Z as xRy as xRy if and only if x 2 + y2 is even. Is this R…

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Q: Consider a relation R on Z- {0} defined by the rule that (x, y) E R if and only if xy > 0. a) Prove…

A: Given the relation R on ℤ-0 defined by         x,y∈R if and only if xy&gt;0.

Q: Let R be a relation on the set A of ordered pairs of positive integersdefined by (x, y) R (u, v) if…

A: Given:

Q: Let Z be the set of integers. Consider R = {(x, y) e Z x Z: 7 divides x-y} S Z x Z. Show that R is…

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Q: A relation R is defined on Z by xRy if and only if 8 divides 3x + 5y. Prove that R is an equivalence…

A: This is a question from relation.

Q: 3. Let R be the relation defined on Z by aRb if and only if 5 | (4a + b). Prove that R is an…

A: We have given relation on ℤ and defined by  aRb if and only if 5|(4a+b). We can  see here for any…

Q: - b if and only if f (a) = f(b). Show that ~ is an Let f: A → B be a surjection. Define a ~…

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Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: b. Define a relation SER XR by S ={ (x,y) E R × R |x – y € Z }. Prove that S is an equivalence…

A: By equivalence relation, we mean that the relation is reflexive, symmetric, and transitive.Here we…

Q: Consider the relation R on Z defined by the rule that (a, b) E R if and only if a + 26 is even.…

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Q: Define the relation on the set Z of integers by if and only if a ~b if and only if a = b + 5k for…

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

A: Concept:

Q: Consider a relation ~ on the set Z such that x~y if and only if x + y is even. The relation ~ is…

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Q: Let the relation non z defined by x ny if and only if 3/(x+2y) Show that n is an equivalence…

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Q: Define a relation on Z by x ~ y if and only if x + 2y is divisible by 3. Show that this relation is…

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Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: Let R be a reflexive and transitive relation on A. Show that RN R¯' is an equivalence relation -1 on…

A: First let, A= set of integers. Then, let, R={(a,b):a,b in A} so,

Q: a Define a relation R on N by (a,b) e Rif and only if EN Which of the following properties does R…

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Q: 3. Define the relation R on Z by mR, if and only if 2|(m – n). Show that R is an equivalence…

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Q: Show that the relation R defined on the set of integers ℤ by (a,b) Î R if a – b = 6k for some k Î ℤ…

A:

Q: on K³defined by: (a, b, c) {0} such that (a, b, c) = k(c, e, d) is an equivalence relation on K3,…

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

Q: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

Q: Define a relation Q on the set R × R as follows. For all ordered pairs (w, x) and (y, z) in R x R,…

A: The relation Q on the set R×R is defined as follows. For all ordered pairs w, x and y, z in R×R, w,…

Q: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

A:

Q: Define a relation R on Z by xRy → x = y + 5k for k E Z. Prove that R is an equivalence relation by…

A:

Q: Problem 17. (a) Prove that <r is a reflexive, transitive relation on P(E*). (b) Prove that =r is an…

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Q: 1. A relation R is defined on Z* × Z* by (m,n)R(p, q) → m+q = n + p . (a). Prove that R is an…

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Q: Let C = {a, b, c, d}. Find a relation R on C that has exactly 3 ordered pair members and is both…

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Q: Consider the relation on Z×(Z\ {0}) defined by (m,n)R(m’,n’) provided that mn’ = m’n. Prove that…

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Q: 4|(x+3y)

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Q: A relation R is defined on R by a R b if a – b e Z. Prove that R is an equivalence relation and…

A:

Q: Let A = {-5, -4, −2, 0, 3, 6, 8), and define an equivalence relation R on A as follows: (x, y) E R…

A: Let A = {-5, -4, -2, 0, 3, 6, 8}, and define an equivalence relation R on A as follows: (x, y) in  R…

Q: Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: A relation R is defined on the set, Z, of integers by xRy if and only if x+ y 2 5. R is A reflexive…

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Q: Let A = Z. Define R to be the relation where a~b if ab > 0. Then R is equivalence relation.

A: We have given the set A = { Z : the set of integers }  R= { (a,b) : a,b belongs to Z and a.b &gt;0}…

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: Define a relation R on Z by declaring that xR y if and only if x^2 ≡ y^2 (mod 4). Prove that R is…

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Q: Define a relation T on R as follows: for all x and y in R, x T y if and only if x2=y2. (a) Prove…

A: Given that a relation T on R such that for all x and y in R, xTy if and only if x2=y2 (a) We have to…

Q: Let a relation R on R2 be given by (x,y)R(x’,y’) provided that x-x’ and y-y’ are integers. Prove…

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Q: Which of the following statements is TRUE? sgn( (5 8) )=1 Let R be a relation on Z defined by xRy if…

A: ?Relation R is not Reflexive, because 2+2=4 does not divisible by 5. So , (2,2) not in R. ?…

Q: 18. Let R be the relation on R defined by xRy → x – y is an integer. Prove that R is an equivalence…

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Q: Let R be the relation on Z defined by x Ry if and only if x+ 3y is even. Prove that R is an…

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Q: Show that the relation R defined on the set of integers ℤ by (a,b) ∈ R if a – b = 6k for some k ∈ ℤ…

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Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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