Explanation Given information: Assume that R and S are relations on a set A and both are transitive. Proof: Let us assume that R and S are transitive and let ( a , b ) ∈ R ∩ S and let ( b , c ) ∈ R ∩ S . By the definition of the intersection, using that ( a , b ) ∈ R ∩ S and ( b , c ) ∈ R ∩ S : ( a , b ) ∈ R ( a , b ) ∈ S ( b , c ) ∈ R ( b , c ) ∈ S By the definition of transitive and using that R is transitive with ( a , b ) ∈ R and ( b , c )

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Chapter 8.2, Problem 39ES

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To prove or disprove that if R and S are transitive, then $R∩S$ is transitive.

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Chapter 8.2, Problem 38ES

Chapter 8.2, Problem 40ES

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To prove or disprove that if R and S are transitive, then R ∩ S is transitive.

Solution Summary: The author explains that R and S are relations on a set A and both are transitive.

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To prove or disprove that if R and S are transitive, then $R∩S$ is transitive.

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Chapter 8 Solutions

To prove or disprove that if R and S are transitive, then R ∩ S is transitive.

Solution Summary: The author explains that R and S are relations on a set A and both are transitive.

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To prove or disprove that if R and S are transitive, then R∩S<m:math><m:mrow><m:mi>R</m:mi><m:mo>∩</m:mo><m:mi>S</m:mi></m:mrow></m:math> is transitive.

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Chapter 8 Solutions

To prove or disprove that if R and S are transitive, then $R∩S$ is transitive.