5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if x- y is divisible by 5. Determine whether R is reflexive, symmetric, antisymmetric and/or transitive. Hence, state whether R is an equivalence relation, a partial order relation or neither.

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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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: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: consider the relation R on R, where R = {(a, b) | a ≤ b+1}. (a) Is the relation R reflexive,…

A: i.Let  then So the relation  holds for all .So  is reflexive.ii.Since the relation is reflexive so…

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 the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Exercise 1.2. Determine whether the following relations ~ is an equivalence relation: (1) nm in Z if…

A: Step 1:Step 2:Step 3: Step 4:

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: a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides…

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Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

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Q: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

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Q: Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3,…

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Q: Consider the relation R on R given by R = {(a, b) | a−b > 3 or a−b = 0}. (a) Show that R is not an…

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

A: Let R be a binary relation on a set A. R is said to be  reflexive if for all . R is said to be…

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…