Let E be an cquivalence relation on Z defined by mEn iF and only iF (mtn) is even, where m,n € Z. IS Find the equivalence classes determine by the elements OF 2 with respect to E.

Q: Select ALL the properties of he relation R = {(1,1), (2,2), (3,3),(1,3)} defined on the set A =…

A: Given A={ 1,2,3}

Q: (a) classes of X induced by Prove that - is an equivalence relation on X and describe the set X/ ~…

A: This is a problem of relation.

Q: . R is the relation defined on Z as follows: m R n ⇒ 4 | (m² – 1 r (1) Prove that R is an…

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Q: Select the following relations on Z that are equivalence relations. O{(a,b)|a>b-1} {(a,b) | a² = 6²…

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Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

A: Given that f:I→R is an monotonic increasing if and only if  f'(x)≥0 for all x∈I The Statement is…

Q: (b) Let A be a partition of X. Prove that R = {(x, y) = X : there exists i such that x € A; and y €…

A: A is a partition of X.R=x, y∈X: there exists i such that x∈Ai and y∈Ai

Q: 9.24. Let R be an equivalence relation on A = {a, b, c, d, e, f,g} such that a Rc, c Rd, d Rg and b…

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Q: Consider the relation being described by the following arrow diagram. Which of the these statements…

A: (i) It is given that ;      S = {6, 7, 8}  and  T = {2, 4, 6} And the relation between S and T is :…

Q: A. Let R be a relation on set A. A={x :xeJ and 0 sx s 12), and R={(a,b) : la - b| is multiple of 4}.…

A: Since not particular question asked, as per guidelines solution to only first question(i.e A) is…

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

A: A relation R defined on a set A is said to be an equivalence relation if the relation R is…

Q: A relation R is defined on Z by a R b if a³ ≡ b³( mod 5). Prove that R is an equivalence relation.…

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Q: R is the congruence modulo 7 relation on Z: For all m, n E Z, mRn iff 7|(m – n). (i) Is the relation…

A:

Q: Define a relation on Z as follows: For m, n € Z, m~n ⇒ 5|(m - n). (5.1) Prove that is an equivalence…

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Q: Let N = {0, 1,2, ...} and let R be a binary relation on the set Z = {(a, b) : a, b e N} defined by…

A: According to our guidelines we can do three subpart of a question please post remaining as a fresh…

Q: (c) For the partial order you identified above, is every pair of elements of Z comparable? (You…

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Q: Let S = {1;2;3;4}, and suppose that ~ is an equivalence relation on S: You are given the information…

A: Given: S=1, 2, 3, 4 and ~ is an equivalence relation on S. Also we have 1~2 and 2~3. To show: There…

Q: 10. (A is the relation defined on Z as follows: for all x, y = Z, x Ay ⇒x=y (mod 3). Describe the…

A:

Q: A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12},  and R={(a,b) :  a - b  is multiple…

A: Since not particular question asked ,as per guidelines solution to only first question (i.e A) is…

Q: Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A…

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Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

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Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: 1 Let R= {(x,e"x): xER,n € Z}. (Here e = 2.71828... as usual.) Prove that R is an equivalence…

A: We see,       For any real number x ∈ IR,             (x, x) = (x, e0.x) ∈ R      Thus, R is a…

Q: 1. Show that R is an equivalence relation on P(A). 2. Set A = {1, 2, 3, 4} and B = {1, 24}.…

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Q: . The relation R on Z defined by a Rb if a? = b² (mod 4) is known to be an equivalence relation.…

A: Consider the given information.

Q: 3) Let S be the equivalence relation on P({0, 1, 2, 3}) defined by XSY if and only if ged(X], 4) =…

A:

Q: Let U = {1,2,3, 4,5} and let A = P(U) be the power set of U. Define the relation R on A by: for 1, Y…

A: Definition:  An element α is said to be an upper bound of a set X, if for every x∈X,  x R α If a is…

Q: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on А.

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