Let - be a relation on N defined as: a ~b if a < (b – 1). (i) Is ~ reflexive? Prove your answer. (ii) Is ~ (iii) Is ~ transitive? Prove your answer. symmetric? Prove your answer.

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

A:

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A:

Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

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

A:

Q: Dominic needs to determine the range for the relation {(1,3), (1,5) , (3,-21), (4, 33)}. What answer…

A:

Q: How can I prove that the relationship r^2 is a subset of r using the definition of composition?

A: The objective of this question is to prove that if r is a transitive relation on a set A, then r^2…

Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

A:

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: How does number 1 differ than a relation? Please explain how, thank you. My teacher wants me to…

A: Relation: Let A and B be two non-empty sets. A relation R from A into B is a subset of A*B.…

Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

A:

Q: Let S = {a, b, c}. Then R = {(a, b)} is a relation on S. Which of the properties reflexive,…

A: Relation R={(a,b)} is defined on set S={a,b,c}A relation R across a set S is reflexive if each…

Q: Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not…

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: (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: Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations…

A: Here we use definition of function and relation