2. Define a relation on Nx N by (n, m) (p, q) Is an equivalence relation? Why? if n+q=p+m.

Q: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

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Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: The relation D is defined on the set P = {6, 9, 15, 54, 78, 90} by the rule: n1 D n2 exactly if (n2…

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: 7. Let (a, b), (c,d) E R2. Define a relation ~on R² by (a, b) (c,d) if 2a - b = 2c-d. (a) Show that…

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Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

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Q: 4. Let R be a relation on the set of all integers. xRy iff x - y = 3m for some integer m. Show that…

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Q: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

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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: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

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Q: Define relations R₁, ..., R₁ on {1, 2, 3, 4} by R₁ = {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3,…

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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: R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R…

A: The question involves finding the transitive closure of a relation R and demonstrating the relation…

Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…

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Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

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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: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

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Q: (a) Show that the relation defined on Z by m~n if 4m +n is divisible by 5 2 is an equivalence…

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Q: 6. (a, b), C

A: Let R be the relation on the set of ordered pairs of positive integers such that a,b,c,d∈R if and…