- #1
roam
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- 12
Homework Statement
Let A,B,C be sets.
(a) Show that:
[tex]A \cup B = (A\B)\cup(B\A)\cup(A \cap B)[/tex]
(b) Show that:
[tex]A \times (B\C) = (A \times B) \ (A \times C)[/tex]
Homework Equations
The Attempt at a Solution
For part (a) I need to prove the definition of a union. I think in order to prove that both sides of [tex]A \cup B = (A\B)\cup(B\A)\cup(A \cap B)[/tex] are equal each other I must show that:
[tex]A \cup B \subseteq (A\B)\cup(B\A)\cup(A \cap B)[/tex] and
[tex]A \cup B \supseteq (A\B)\cup(B\A)\cup(A \cap B)[/tex]
I'm stuck here and don't know how to prove that the two are subsets of one another. Can anyone help me please?