(a) Give complete definitions of the terms (i) Cartesian product of two sets; (ii) relation on a set; (iii) equivalence relation on a set.

Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: (b) Define Equivalence Relation with an example. Give an example of a relation which is not…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: Using properties of sets, show that(i) A ∪ ( A ∩ B ) = A                                (ii) A ∩ ( A…

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Q: Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation…

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Q: 3. On the relation R on the set {1, 2, 3, 4, 5} defined by the rule (x, y) e R if x+y<6. a) List the…

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Q: Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS…

A: If PQ≅RS then by definition, d(P,Q)=d(R,S)...(equation 1) and if RS≅UV then by definition,…

Q: 1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b…

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Q: Given set A = {1, 2, 3} and S = P(A) The relation is defined as xRy ⇔ |x| = |y| Indicate the…

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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: Consider following relations on the set of positive integer: R₁ = {(a,b) | a> b} R₂ = {(a,b) | a = b…

A: The objective of the question is to determine which of the given relations are symmetric and…

Q: Triangle theorem 1. Congruence of triangles is an equivalence relation. Prove triangle theorem 1.

A: A detailed solution is given below.

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

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: (a) (AUB)\C= (A \C)U(B\C)

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Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: Exercise: Let R be a relation on people such that (a,b) is" a is a parent of b Let S be a relation…

A: Let R be a relation on people such that (a,b) is "a is a parent of b".Let S be a relation on people…

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: Please answer the part (B). I have got a solution for the question on this platform but the answer…

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Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: R is a relation on set of integers (Z) and it is given by Then, R is (x, y) = R⇒ |x − y| ≤ 1.…

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Q: 1(b). Is (p->q)->[(p->q)->q] a tautology? Why or why not?  (c). Given the relation on the set .…

A: We are entitled to solve only one question at a time. Please submit another question separately. To…

Q: 0 = A = possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If it is not…

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Q: prove why they have or do not have the properties: reflexive, symmetric, antisymmetric, transitive…

A: A=a,b,cR=a,a, b,b, c,c, a,b, a,c, c,b A relation R is reflexive if a,a∈R for every element a. Here…

Q: Discrete Structure (Math) 22(i). Let A = {2,3} be a non-empty set. If R = {(a, b) : a ≤ b and a, b =…

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Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

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Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider…

A: Given that, The relation is “same age” and the set is cars made in 2015, 2016,2017, 2018, 2019, and…

Q: (a) Define the following terms: (i) Cartesian product of two sets; (ii) relation on a set X. (b)…

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