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Homework Statement
Let A and B be relations on the set C = {1,2,3,4,5,6}. Prove or disprove the following:
If A and B are symmetric, then A U B is symmetric.
Homework Equations
The Attempt at a Solution
The main problem is that I don't know how A U B is defined.
In general, a relation R is a subset of A x B. For example, {(1,1), (1,2)} is one relation. (ie. I can write 1 R 1, and 1 R 2.)
Symmetric means that for all x, y in C, if x R y then y R x.
I know A U B would be read "A or B", but I don't understand it? Is it like (x A y) or (x B y)?
Then I don't get what A U B would look like if it was symmetric.
Then to prove it you suppose that if x A y then y A x. You also suppose that if x B y then y B x.
From here I don't know what I'm supposed to show...