Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y ∈N}. Depict this relationship using roster form. Write down the domain and the range.

Q: Determine if the relation ? = {(f, g)|f(x) = g(x) for some x ∈ ℝ} on the set of all functions from ℝ…

A:

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b): a < b?.…

A:

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: Show that the relation R on a set A is symmetric if and only if R = R-, where R is the inverse…

A:

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

A:

Q: A relation R is defined on the set of real numbers by xRy if and only if x-y is a multiple of 3.…

A:

Q: Let A = {1, 2, 3, 4, 5, 6}. Define a relation R from A to A by R = {(x, y) : y = x + 1 }(i) Depict…

A:

Q: List the ordered pairs in the relation R from A = 0, 1, 2,3,4, B = 1,2,3, 4, 5, where R is defined…

A: Relation : A relation from a set A to a set B is a subset of A×B. i.e. a relation R consists of…

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: Reflexivity: Since x≠x+2 , therefore, (x,x)∉R and hence R is not reflexive.   Symmetricity: Let…

Q: 4. Let R be the relation in the positive integers

A: 4. Given, R be the relation in the  positive integers ℕ defined by                        R=x, y: x,…

Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: Let the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

A:

Q: Does the relation "is a friend of" have a reflexive property (consider one person)? A symmetric…

A: Does the relation "is a friend of "  have a reflexive property (consider one person)?

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b) : |a –…

A: Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b)…

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

A:

Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

A:

Q: - List the ordered pairs in the relation R from A = (0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b)…

A:

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

A:

Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

A:

Q: List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B {0, 1, 2, 3}, where (a,b) e R…

A:

Q: Suppose that the relation H is defined as follow. H=(7,7),(0,-1),(3,9),(-9,3). Give rhe domain and…

A:

Q: Define a relation S from R to R as follows:…

A:

Q: Express the set W = {q|q 2} using interval notation. Use "U" for or .

A:

Q: Determine whether the following relations are equivalence relations. For those relations that are…

A: Consider the given relation is given as:

Q: Define the relation R on 72 = Z x Z by (a, b) R (c, d) if a + d = b+ c. Prove that R is ar…

A:

Q: Let N be the set of natural numbers and the relation R be defined onN such that R = {(x, y) : y =…

A: Let N be the set of natural numbers and the relation R be defined onN such that R = {(x, y) : y =…

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

A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

Q: Define a relation P from R to R as follows.for all real numbers X and Y with X>0 (X,Y)€P means that…

A:

Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

A:

Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

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: The domain for the relation A is the set {2, 5, 7, 8, 11}. For x, y in the domain, xAy if |x-y| is…

A:

Q: Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

A: Prime numbers less than 10 are 2,3,5,7

Q: The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: Reflexive Relation: A relation R on a set A is said to be reflexive if  (a,a)∈R   for every a∈A.…

Q: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

Q: 3. Find all ordered pairs in the relation R from A = (a,b) E R if and only if a + b = 9. {0,2,4,7}…

A:

Q: Suppose that the relation H is defined as follows. H= {(4, p), (8, 0), (5, p)} Give the domain and…

A:

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

A:

Q: Let ℝ denote the set of real numbers, and  β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which…

A: The given relation β⊂ℝ2 is: β=x,y∈ℝ×ℝ | xy≥0 The properties of a relation is: Reflexive Irreflexive…

Q: List the coordinate pairs needed in order to turn the following relations into equivalence…

A:

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

A:

Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

A:

Q: Determine the domain and range of the relation R defined byR = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4,…

A: We make a table for the relation x x+5 0 5 1 6 2 7 3 8 4 9 5 10

Q: Define a relation Pfrom R+ to R as follows: For all real numbers x and y with x> 0, (x, y)E P means…

A: Introduction: A relation is a subset of Cartesian products of two sets. In each ordered pair, there…

Q: Consider a relation R on Z = {3,4,5,6} is defined by pRq iff 2p + q is even. a) Please list the…

A:

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

A:

Q: Let A = {1, 2, 3, 4, 5} Determine whether the relation R whose diagraph is given is relflexive,…

A: A relation R is said to be reflexive on the set A if for every element x in the set A, the ordered…