determine whether the relation R on the set of all reflexive, symmetrical, antisymetric, and or transitive integers, where (x,y) ε R if and only if: a. x ≠ y b. xy ≥ 1. c. x = y + 1 or x = y-1 d. x ≡ (mod 7)

determine whether the relation R on the set of all reflexive, symmetrical, antisymetric, and or transitive integers, where (x,y) ε R if and only if: a. x ≠ y b. xy ≥ 1. c. x = y + 1 or x = y-1 d. x ≡ (mod 7)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....

See similar textbooks

Related questions

Q: 1) If A = 2 -1 and B = 1 -2 7 0…

A: We are given A=[2-17 0], B=[1-23-3]

Q: . A finitely additive measure u is a measure iff it is continuous from below as in meorem 1.8c. If…

Q: If gcd(m,p) = 1 and p is prime, show that gcd(m,pk ) = 1 for all k≥ 1.

A: To show, If gcd(m, p)=1 and p is prime, show that gcd(m, pk) = 1 for all k≥1.

Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

Q: Find the solution of the initial value problem 1 11y" — 12y + y = 0, y(0) = 11, y'(0) 11 Then…

Q: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

Q: Since it's an if and only if proof, don't you have to prove "if linearly dependent, then scalar…

Q: Find the general solution of the differential equation y(4) - 4y" = t² + et.

Q: Suppose that a company that makes sweatshirts has a linear demand function of qD = –13p + 500 and a…

Q: Find the interval of convergence of the following series: x- - x5 3 5 7 +3 + x7 + O-2<x<2 O-3<x<3 O…

Q: Use symbols (syembolize) for the next lines and construct prooof to the argument All doctors and…

A: The symbols given are represented as follows, Dx: x is a doctor Dx is set of doctorsPx: x is…

Q: or a region R in the xy-plane with boundary C, show that Green's theorem can be itten as: fonds =…

A: Here we have proved the given condition by Green's Theorem.

Q: Consider the subspace spanned by A ---- and 7₂ and the vector = basis {1, ₂}. = 5 9 in this…

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these…

Q: Maximize p = x + 3y subject to the following constraints. x - 4y ≤0 4x - y ≥ 0 x+y≤ 10 x ≥ 0, y ≥ 0…

Q: Solve the initial value problem y" + 4y' — 12y = 0, y(0) = a, y′(0) = 60. Find a so that the…

Q: Solve the following PDES: u,= K² u.,

A: The given problem is to find the solution for the given heat equation partial differential equation.

Q: A company that makes sweatshirts is willing to supply 156 sweatshirts each month if the price is $24…

Q: Solve using the simplex technique, and then identify the optimal values of these variables Z, x1,…

A: After using slack variable we have Max Z=4x1+2x2+5x3+0S1+0S2+0S3Subject…

Q: Find the perimeter of the parallelogram shown below 43 51 48

A: the perimeter of parallogram when two sides are given= 2(a+b) where a and b are adjacent sides

Q: Find the interval of convergence of the follow X + x² 2 x 3

Q: Consider the following initial value problem. Determine the coordinates tm and ym of the maximum…

A: Sol

Q: Solve the initial value problem y" - 4y' — 21y = 0, y(0) = a, y′(0) = −24. Find a so that the…

Q: Write TRUE if the truth value of the statement is incorrect, otherwise write FALSE. All dogs are…

A: Truth table:- p q p⇒q p⇔q T T T T T F F F F T T F F F T T Part (1):- Given…

Q: A four digit number is to be formed from the digits 0, 2, 5, 7, 8. How many numbers can be formed if…

Q: Let A and B be two events such that p(A) = 0.4 and P(BA) = 0.2. Then P(BnA) = 0.4 0.7 0.6 0.5

Q: A university math department offers courses in College Algebra, Finite Mathematics, and Applied…

Q: 3. (True/False) If f(x, y) has a local minimum and is differentiable at (a, b), then fu(a, b) any…

A: Since you have asked a question with multiple subparts so as per guidelines will solve the first…

Q: Suppose that X has a discrete distribution with the following probability distribution function 0…

A: We want to find the value of a and b

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: (i) (1, 1), (-6,0), (-2, 2), (-2,-8)

Q: Find the Laplace of f(t) = (t− 2)(t+2)e-³t

Q: (c) Translate the pulse, i.e. move the nonzero value of the func- tion to a different location while…

A: As per the question we are given a rectangular pulse signal f(t) and we have to : Find the Laplace…

Q: a) An engineering problem is modelled by the formulae below. If the distance travelled by some…

A: Given integration is I=∫0πsin(x)dx Here f(x)=sinx Number of subinterval is n=10 Then step size is…

Q: What function is this? What changes do you see? List them What does a= b= c= So the function is…

A: Consider the given figure. For the interval -∞,2. Here, the graph is a straight line. Take…

Q: Find the sum of natural numbers from1 to 100. 2. Find S12 , the tenth partial sum of the

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: a. Find the Maclaurin series for x sin (x²) b. Approximate the value of 0.1 sin(0.01) using the 7th…

Q: . Represent the following sets in the Gaussian plane: (a) {z EC Rez 2 A 2-1+2i <3}

Q: Consider the function f(x) = 6 - 4x² on the interval [3, 7]. Find the average or mean slope of the…

Q: - 2 How did he get the value inside the circle X(t) = 1- -t W₁ = 2 = 21. 2 = 2TT 2포 T xt) = 1-t,…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: The region is bounded by the graph of the equations y=x, y=0, x=1. Draw the region. Draw the graph…

Q: Consider the weighted voting system [7: 7, 4, 2]. Find the Shapely-Shubik Power distribution.…

Q: A fair dice is rolled twice. The probability that the outcomes on the dice are different given that…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Given the differential equation y4+2y''+y=3sint

Q: 1-a) Use Runge Kutta fourth order method to integrate y'= 4e0.8² -0.5y from t=0 to 3.0 S with step…

A: Given IVP is y'=4e0.8t-0.5y y(0)=2 step size h=1 So by Runge-Kutta method of order 4,…

Q: Find the order of the element (2, 3) in the direct product group Z4 × 28. Compute the exponent and…

Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: C. Determine the radius and the interval of convergence for the given power series: a. (x-2)3(x-2)5…

Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

Q: A child psychologist is interested in the number of times, x, a newborn baby's crying wakes its…

Question

determine whether the relation R on the set of all reflexive, symmetrical, antisymetric, and or transitive integers, where (x,y) ε R if and only if:
a. x ≠ y
b. xy ≥ 1.
c. x = y + 1 or x = y-1
d. x ≡ (mod 7)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .
Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
For each of the following relations R defined on the set A of all triangles in a plane, determine whether R is reflexive, symmetric, or transitive. Justify your answers. a. aRb if and only if a is similar to b. b. aRb if and only if a is congruent to b.
In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A. Determine in each case whether R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if xy. b. xRy if and only if xy.