- #1
kathrynag
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Homework Statement
Prove:
(A-B)[tex]\cup[/tex](B-A)=(A[tex]\cup[/tex]B)-(A[tex]\cap[/tex]B)
Homework Equations
The Attempt at a Solution
We need to show (A-B)[tex]\cup[/tex](B-A)[tex]\subseteq[/tex](A[tex]\cup[/tex]B)-(A[tex]\cap[/tex]B)
and (A[tex]\cup[/tex]B)-(A[tex]\cap[/tex]B)[tex]\supseteq[/tex](A-B)[tex]\cup[/tex](B-A).
We begin by showing the first:
Let x[tex]\in[/tex](A-B)[tex]\cup[/tex](B-A).
By definition of union, x[tex]\in[/tex]A-B or x[tex]\in[/tex]B-A.
If x[tex]\in[/tex]A-B, we know x[tex]\in[/tex]A ...
This is where I've begun to get stuck. Not sure where to go next.