Explanation Given information: Let A be the set of people living in the world today. A relation R is defined on A as follows: For all p, q ∈ A, p R q ⇔ p lives within 100 miles of q. Calculation: A = set of people living in the world today R = { ( p , q ) ∈ A × A | p lives within 100 miles from q } Reflexive: The relation R is reflective if ( p , p ) ∈ R for every element p ∈ A . Since a person always lives within 100 miles from itself, we know that ( p , p ) ∈ R for all elements p ∈ A . thus R is reflexive. Symmetric: The relation R on a set A is symmetric if ( q , p ) ∈ R whenever ( p , q ) ∈ R . Let us assume that ( p , q ) ∈ R

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Chapter 8.2, Problem 31ES

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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 30ES

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

Solution Summary: The author explains that the relation R on a set A 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