But how to simplify further? Would be grateful for any help. Thanks!
(a AND not b) OR (not a AND b)
This is just equivalent to (a xor b), not the initial formula.
But, it turns out that all you need is the left disjunct.
That's the (perfect) disjunctive normal form for the initial formula.
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Simplifying a term 
![\begin{array}{ccc}a \cap \bigg[(a \cap b') \cup (a' \cap b)\bigg] & & \text{Given} \\ \\ \bigg[ a\cap (a \cap b')\bigg] \cup \bigg[a \cap(a'\cap b)\bigg] && \text{Distributive} \\ \\ \bigg[(a\cap a) \cap b'\bigg] \cup \bigg[(a\cap a') \cap b\bigg] & & \text{Associative}\end{array}](http://www.mathhelpforum.com/math-help/latex2/img/a192a4bd49288344c7022bb806e0ece9-1.gif "\begin{array}{ccc}a \cap \bigg[(a \cap b') \cup (a' \cap b)\bigg] & & \text{Given} \\ \\ \bigg[ a\cap (a \cap b')\bigg] \cup \bigg[a \cap(a'\cap b)\bigg] && \text{Distributive} \\ \\ \bigg[(a\cap a) \cap b'\bigg] \cup \bigg[(a\cap a') \cap b\bigg] & & \text{Associative}\end{array}")
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