a. Define a relation Ron Z as follows: For all integers m and n, mRn ⇒ 3|(m − n). Then 3R5 (A) True (B) False b. With R defined as above, 5 R8 (A) True (B) False c. With R defined as above, R is symmetric. (A) True (B) False

Q: Please do the following questions with handwritten working out

A: Step 1: Step 2: Step 3: Step 4:

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A: We solve this using counter examples .

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A: Given a relation R on the set of all integer numbers defined by R={(x, y)∈Z×Z:x-y≤2}.  We have to…

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A: (i) The relation D is defined on the set P=6, 9, 15, 54, 78, 90 by the following rule: n1 D n2…

Q: Let R be a relation over the positive integers defined as follows: R = {(a,b) | 2b < a < 3b }…

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

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Q: Consider the following relations: R₁ = {(a, b) € R²1 a> b), the greater than relation R₂ = ((a, b) =…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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

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A: A relation R between two sets A and B is the set of all ordered pairs a,b such that a∈A and b∈B. We…

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Q: Define the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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Q: . Define a relation R on Z as follows: a Rb if and only if 5 | (a²- 6²). Find four integers which…

A:

Q: Consider the relation R = {(1,1);(2,3);(3,5);(4,7)}. a. Prove that R is a function from {1,2,3,4}…

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Q: Please do the following questions with handwritten working out.

A: Step 1:You're absolutely right! Here's the proof that the intersection of two transitive relations…