Discrete Math 12. Consider the relation Con R given by xCy if and only if x...
3) Define the relation <on R via x < y if and only if xy < 10. Show that is symmetric. (20 points)
4. Consider the relation on the positive integers xRy if and only if x x+y (a) List three ordered pairs from this relationship (b) Is R reflexive? Prove your answer (c) Is R symmetric? Prove your answer (d) Is R anti-symmetric? Prove your answer (e) Is R transitive? Prove your answer.
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite 9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...
Complete the proof of Theorem 4.22 by showing that < is a transitive relation. Let R be a transitive relation that is reflexive on a set S, and let E-ROR-1. Then E is an equivalence relation on S, and if for any two equivalence classes [a] and [b] we define [a] < [b] provided that for each x e [a] and each y e [b], (x, y) e R, then (S/E, is a partially ordered set.
10. [12 Points) Properties of relations Consider the relation R defined on R by «Ry x2 - y2 = x - y (a) Show that R is reflexive. (b) Show that R is symmetric. (c) Show that R is transitive. (d) You have thus verified that R is an equivalence relation. What is the equivalence class of 3? (e) More generally, what is the equivalence class of an element x? Use the listing method. (f) Instead of proving the three...
Is this reflexive, symmetric, and/or transative? Define the relation 3 over R where rSy if and only if x-y є Q. Is g reflexive, symmetric, and/or transitive? Explain why.
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if a) x + y = 0 b) x= ±y. c) x-y is a rational number. d) = 2y. e) xy ≥ 0. f) xy = 0. g) x=l. h) r=1 or y = 1
Math 240 Assignment 4 - due Friday, February 28 each relation R defined on the given set A, determine whether or not it is reflexive, symmetric, anti-symmetric, or transitive. Explain why. (a) A = {0, 1,2,3), R = {(0,0).(0,1),(1,1),(1,2).(2, 2), (2.3)} (b) A = {0, 1,2,3), R = {(0,0).(0,2), (1,1),(1,3), (2,0), (2,2), (3,1),(3,3)} (c) A is the set of all English words. For words a and b, (a,b) E R if and only if a and b have at least...
3. (12 pts) Determine whether the following binary relation is: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive. a) The relation Ron Z where aRb means a = b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive? Yes or No Yes or No Yes or No Yes or No b) The relation R on the set of all people where aRb means that a is taller than b. Circle your answers. (4 pts) Ris Reflexive? Symmetric? Antisymmetric? Transitive?...
number theory and discrete math show full steps Find Gaussian integers a+ib and r+is such that 234212 + 3421 i - (23+ 41i) (a + bi) + (r + si) such that 2 (72 +82) < 232 + 412.