Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence relation?

Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: (a) Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z ×…

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Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is:    (a) reflexive and symmetric,…

A: Let A=1,2,3,4. To give an example of a relation on A that is:  (a) reflexive and symmetric, but not…

Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: . A) Write the ordered pairs, graphical representation, and the relation matrix, for  the Relation R…

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Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,b),(b,b),(b,c)(c,a)(c,c) and…

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, a),…

Q: 2. Let R = {(x, y) = R x R = |x] + [y] =4}. Then R is a relation on R. Is R an equivalence relation…

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Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: Determine whether the relation R is a partial order relation on the set of positive…

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Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

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Q: Show that if R and R2 are equivalence relations on A, then R1 n R2 is an equivalence relation on A.

A: Equivalence relation on a set A

Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: (2.3) Prove that R is an equivalence relation.

A: Prove R is an equivalnce relation.

Q: Let T be the relation defined by, For all a, b e Z, aTb iff a – b is odd. Is T an equivalence…

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Q: Let R be the relation over the set of all people where aRb iff a is the same age as b. Determine and…

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Q: What is the reflexive closure of the relation R = {(a , b) I a < b} on the set of integers

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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…

Q: Let the relation R defined on the set of positive integers as (x, y) ER if 3 divides X - y Determine…

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Q: Let A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3) and define a relation R on A as follows: For all x, y…

A: Given : A = {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3} and R is an equivalence relation on A defines as ;…