Explanation Given information: Let A be the set of all English statements. A relation I Is defined on A as follows: For all p, q ∈ A, p I q ⇔ p → q is true. Calculation: A = Set of all english statements I = { p , q ∈ A | p → q is true } Reflexive: The relation I Is reflective if ( p , p ) ∈ I for every element p ∈ A . Let p be an English statement. If p is true, then p → p is true, since both (sub) proportions are true. If p is false, then p → p is true, since the if-statement is false. Thus p → p is always rue, which implies that ( p , p ) ∈ I and thus I Is reflexive. Symmetric: The relation I on a set A is symmetric if ( p , q ) ∈ I whenever ( q , p ) ∈ I Let us assume that ( p , q ) ∈ I , by definition of I: p → q is true However, when p is false and q is true, then q → p will be false and thus q → p is not necessarily true, which implies that I Is not symmetric

5th Edition

ISBN: 9780357540244

Author: EPP

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 8.2, Problem 27ES

To determine

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 26ES

Chapter 8.2, Problem 28ES

Students have asked these similar questions

Let F = V where (x, y, z) x2 1 + sin² 2 +z2 and let A be the line integral of F along the curve x = tcost, y = t sint, z=t, starting on the plane z = 6.14 and ending on the plane z = 4.30. Then sin(3A) is -0.598 -0.649 0.767 0.278 0.502 0.010 -0.548 0.960

Let C be the intersection of the cylinder x² + y² = 2.95 with the plane z = 1.13x, with the clockwise orientation, as viewed from above. Then the value of cos (₤23 COS 2 y dx xdy+3 z dzis 3 z dz) is 0.131 -0.108 -0.891 -0.663 -0.428 0.561 -0.332 -0.387

2 x² + 47 The partial fraction decomposition of f(x) g(x) can be written in the form of + x3 + 4x2 2 C I where f(x) = g(x) h(x) = h(x) + x +4

Chapter 8 Solutions

WEBASSIGN F/EPPS DISCRETE MATHEMATICS

Ch. 8.1 - If R is a relation from A to B, xA , and yB , the...Ch. 8.1 - Prob. 2TY Ch. 8.1 - Prob. 3TY Ch. 8.1 - Prob. 4TY Ch. 8.1 - If R is a relation on a set A, the directed graph...Ch. 8.1 - As in Example 8.1.2, the congruence modulo 2...Ch. 8.1 - Prove that for all integers m and n,m-n is even...Ch. 8.1 - The congruence modulo 3 relation, T, is defined...Ch. 8.1 - Define a relation P on Z as follows: For every...Ch. 8.1 - Prob. 5ES

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Solution Summary: The author explains that the relation I on a set A is reflexive, symmetric, transitive or none of these.

Videos

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Want to see the full answer?

Chapter 8 Solutions