In 37-42, assume that R and S are relations on set A. Prove or disprove each statement.
If R and S are transitive, is transitive? Why?
To prove or disprove that if R and S are transitive, then is transitive.
Assume that R and S are relations on a set A and both are transitive.
Let us assume that R and S are transitive and let
By the definition of the intersection, using that
By the definition of transitive and using that R is transitive with
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