Explanation Given information: Let X = { a, b, c } and P(X) be the power set of X. A relation L Is defined on P(X) as follows: For all A, B ∈ P(X), A L B ⇔ the number of elements in A is less than the number of elements in B. Calculation: Consider the given set X = { a , b , c } Let us consider that A = P ( X ) The relation L Is given by L = { B , C ∈ P ( X ) | B has less elements than C } Reflexive: The relation L Is reflective if ( B , B ) ∈ L for every element a ∈ A . Since A = P ( X ) , L Is reflexive if it contains ( B , B ) for all B ∈ P ( X ) . We note that E does not contain ( B , B ) because a set never has less elements than itself and thus E is not reflexive. It is not reflexive Symmetric: The relation L on a set A is symmetric if ( C , B ) ∈ L whenever ( B , C ) ∈ L Let us assume that ( B , C ) ∈ L , by definition of L : B has less elements than C

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Chapter 8.2, Problem 21ES

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

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Chapter 8.2, Problem 20ES

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Chapter 8 Solutions

Discrete Mathematics With Applications

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

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

Solution Summary: The author explains whether the given relation is reflexive, symmetric, transitive or none of these.

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

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Chapter 8 Solutions