# Homework Help: Symmetric difference problem (Real Analysis)

1. Aug 28, 2010

### phillyolly

1. The problem statement, all variables and given/known data

What am I asked to do in the problem? Am I just asked to draw a diagram or to prove a) and b)?

2. Relevant equations

3. The attempt at a solution

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2. Aug 28, 2010

Draw a Venn diagram with sets A and B. Shade in the area "that belongs to either A or B, but not both."

Then, I'd say just make sure you first know exactly what (a) means, i.e., what is A\B and B\A. You should easily be able to see that the definition of D in (a) is the same as the more intuitive definition "either A or B, but not both."

Finally, you should write a quick formal proof that shows the definition in (a) is the same as that in (b).
i.e, prove that (A \ B) U (B \ A) = (A U B) \ (A $$\cap$$ B).

Since you're new to all of this, don't skip steps. Take care of the details!

3. Aug 28, 2010

### phillyolly

Thank you.....

Based on your suggestions...I tried...Where is my mistake?

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4. Aug 28, 2010

Thirdly, $$x \in A \backslash x \in B$$ is also utterly meaningless. The relative complement operation "\" is defined only on sets.
$$x \in (A \backslash B) \cup (B \backslash A).$$
$$x \in (A \backslash B) \vee x \in (B \backslash A).$$
$$(x \in A \wedge x \notin B) \vee (x \in B \wedge x \notin A).$$