In 37-42, assume that R and S are relations on a 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.
Given statement: Let R and S are relations on the set A. If R an S are transitive, then is transitive
The given statement is false, which we will justify with a counterexample.
By the definition of the union:
R is transitive, because the if-statement “
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