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

Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

Q: Find the domain of the function ∑ akzk from k = 0 to k = ∞

A:

Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: Label the relations below as reflexive (or not), symmetric (or not), antisymmetric (or not), and…

A: A) ONLY antisymmetric

Q: f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is…

A: Use the definition of antisymmetric to check whether the given relation is antisymmetric or not.…

Q: 3. Use finite differences to determine whether each relation is linear, quadratic, or neither. a) y…

A: To determine if the relation is linear, quadratic, or neither.

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A:

Q: Scanned.47thDetermine if the relation r CS CamScannegymmetric, antisymmetric or neither

A: The relation R is said to be symmetric if any ordered pair (x,y) ϵ R then the ordered pair…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: For a,bEN define the relation a -b if and only if ab is a perfect square. Is this relation…

A:

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: Find the solution to this recursive relation  an=2nan-1, a0=3

A: Given that  an=2nan-1, a0=3 To find the solution of this recursive relation

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

A:

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

A:

Q: For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: Define a relation R on Z as follows: For all integers m and n, m R n 5| (m² – n²). a. Is 1 R (–9)?…

A:

Q: - whether the following relation is a functio- x² – 2x + 1

A: We have to identify  the given  relation is function  not

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

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 < b³}.…

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

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

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Q: Is Ra partially ordered relation ? ? . Why ?..

A: Solution is below provided

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

A: See the detailed hand written solution below.

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: 1. Consider the relation R1: R - R such that (r1, y1)R1 (X2, y2) if and only if both points are on…

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

A: This relation is Discrete.

Q: Determine the minimum for the relation y (x + 16)(x - 8). -64 -16 -226 -144

A: To determine- minimum  for the given relation.

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: Find the characteristic equation of the recursive relation an 송,Mn 2 1. O 3r – 1=0 Or+3=0 Or-3= 0…

A:

Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: Write the domain of the relation y = arccsc x. x≤-1 or x≥1 -1≤x≤1 0≤x≤1

A:

Q: Determine if the relation defines y as a ône-to

A: The given graph is: To determine if it is one-to-one.

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 the relation R over integers as follows: R = { (a, b) | |a - b| < 5 } Determine if R is (a)…

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Q: Give an example of a relation which is a) One-one and onto b) Many - one and onto c) One-one and…

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Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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: Is this relation

A: Using definition of relation

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

A:

Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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Q: Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.

A:

Q: The algebraic translation of "x is no less than 7" is .

A: Given statement is "x is no less than 7:. To translate into algebraic form. Solution: Given that x…

Q: (b) The domain of the relation A is the set of all real numbers. XAy if |x-y| <2

A: b. To check the reflexive, for any x∈ℝ then, x-x=0≤2 That is, for all x∈ℝ, xAx. Therefore, A is…

Q: Define a relation R on Z as follows: For all integers m and n, m Rn = 5|(m² - n²). (a) Is 1 R (-4)?…

A:

Q: Suppose that R is a relation. Show that R C dom(R)×ran таn(R).

A: Given R is a relation. Let R be relation on a set A. Now define domain and range of relation R as…

Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

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

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…