Let A = {1, 2, 3) and B = {4, 9, 21, 25). Define the relation R from A to B by a R b if a divides b. (We say a divides b if there is an integer m such that b = am. In other words, a is a factor of b or b is a multiple of a). List all the members of R. [Hint: (2, 4) belongs to R since 2 divides 4.]

Q: Let A = { 2, 3, 4 } and B = { 6, 8, 10, 12 } and define a relation R from A to B as follows: %3D For…

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Q: b) Let A = {0, 1, 3,4, 5, 6} and define the relation R and S on A as follows: For every (x, y) €A,…

A: all the ordered pairs (x,y) in the relation R and S and SoR are given below...

Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

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Q: Determine whether the following statements are True or False: a - For all relations R and S, ROS=SOR…

A: We solve this using counter examples .

Q: 1. Suppose we would like to define a function f : Q→ Z by the formula f(r) = a +b, where a, b € Z…

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Q: 5. Identify each relation as linear, quadratic, or exponential. a) YA b) c) -4 -20 +2 -6 4 4 6 2 YA…

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Q: b. Explain that is {(1, 3), (2, 2), (3, 1)} a permutation function on set A = {1, 2, 3}? if it is a…

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Q: Let A = {1,2,3,4} and B = {5, 6, 7). Let f be the relation f = {(1,5), (2,5), (3, 6), (?, ?)} where…

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Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: = Let a, b, and d be positive integers. Prove that if (a, b) : divides a, then (d, b) = 1.

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Let A = {4, 5, 6} and B = {6, 7, 8} and let S be the "divides" relation from A to B. That is, for…

A: Here given sets A = {4, 5, 6} and B = {6, 7, 8} and relation defined asxSy⇒x/y means x, y∈S⇒x…

Q: Given set A={1,2,3,4,5} and a relation R on set A, R = {(1,2), (1,3), (2,2), (2,4), (3,1), (3,5),…

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Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

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Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: for the following relations on 2 the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)},…

A: A relation R is an equivalence relation if it is: i) Reflexive: if aRa for all a in A ii) Symmetric:…

Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: %3D For all (x, y) E A × A, (x,…

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Q: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

Q: II.5 Determine whether relation R on the set of all real numbers is reflexive, symmetric,…

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Q: Let V be all elements of R2 that have the form (a, a2) where a is a real number. Show that (3,9) is…

A: Let V be all elements of R2 that have the form (a, a2) where a is a real number. We have show that…

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by a R b if and only if a < b. (a) Compute R²…

A: use the concept of composition          R2=RoR          R3=R2oR

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: Which of the following relations E are equivalence relations on the set of integers Z? 3. a. xEy if…

A: A relation E on a set A is called E is reflexive if xEx, ∀x∈A. E is symmetric if xEy, implies that…

Q: Let A = {12, 13, 15, 16} and B ={13, 15, 17}, and let the relation R from A to B be defined by…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Another operation that can be defined on sets A and B is the difference of the sets, denoted by A −…

A: First we have to find B' (complement of B)

Q: Find a function from the set {1,2,.....30} to {1,2,.....10} that is a 3-to-one correspondence.

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