Homework Statement
Let R be a reflexive and transitive relation on a set A. Define another relation, S, such that, for any x, y ∈ A, Sxy iff (Rxy and Ryx).
Prove:
S is an equivalence relation on A.
Homework Equations
S is an equivalence relation if it is symmetric, reflexive and...
You two are my heroes. I started looking into the more because I believed the same thing. I copied the question from my online class system into this forum, but then I found that he had entered the questions online wrong. Else where in our class literature, the question is written as ((A ∪ B) ∩...
Hi Everyone!
I would really appreciate some help with this set proof.
Homework Statement
Show that, for any sets A, B, ((A ∪ B) ∩ A) = (A ∩ A') ∪ (A ∩ B).
(Hint: Remember that a complement of a complement is just the original set.)
Homework Equations
I can use any sentential...