Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

Q: Show that AB→C does not logically imply A→C, nor B→C.HINT: Write a relation instance that satisfies…

A:

Q: Consider  the relation R={(a, b),(a, c),(c, b),(b, c)} on  the set A={a, b, c}. Is R reflexive? Is R…

A:

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: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

A:

Q: Every equivalence relation is reflexive. True False

A: A relation is said to be an equivalence relation if and only if the relation R is reflexive,…

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

A:

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

A:

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

Q: {(a, b) acb, a and b are finite set of integers}

A:

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

Q: Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b} is an…

A: Given, the relation R in the set Z of integers given by R = {(a, b) : 2 divides a– b}.

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

A:

Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: Đ A is a closed set.

A:

Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

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. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

A:

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

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

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

Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

A:

Q: Consider the set Q = Z × (Z 10), and the relation fupon Q Defined as: (a, b) ↑ (c, d) + a•d = b•c a)…

A: we shall solve the part (a) only , if you want us to do other parts please resubmit the question…

Q: Define a relation on the set {a, b, c, d} that is 6. (a) irreflexive and transitive, but not…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

A:

Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

A:

Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

A:

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: Draw the Hasse diagram for the relation C on the set P({1,2,3}).

A: According to the given information, it is required to draw the hasse diagram for the given relation.

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

A:

Q: Determine, with justification, whether the following relations are equivalence relations. If so,…

A:

Q: Define: what is an equivalence relation?

A:

Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

A: Let R be a relation on a set A. Then R is said to be an equivalence relation if it is reflexive,…

Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

A:

Q: Let A be a set and R be a reflexive relation on A. Prove that R is an equivalence relation if and…

A:

Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

A:

Q: Consider the set Q = Z ×(Z 10), and the relation tupon QDefined as: (a, b) ↑ (c, d) e a·d=b·c a - d…

A:

Q: '17. Prove or disprove: Let R be an equivalence relation defined on a set A. For any x, y E A,…

A: Given result is: '' Let R be an equivalence relation defined on a set A. For any x,y∈A, either x∩y=∅…

Q: Give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not symmetric, and…

A: We need to give an example of a relation over the set {0, 1, 2, 3} that is not reflexive, not…

Q: . Let R be a relation defined on the set A = N x N where (a, b) R (c, d) if a³ s an equivalence…

A: Introduction: Any two elements are said to be equivalent if they have an equivalence relationship. '…

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

A:

Q: Let S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an equivalence…

A:

Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

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

A: image is attached