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## Main Question or Discussion Point

I was trying a while ago to prove associativity of the XOR operator. That led me to the following problem:

I am trying to prove [tex] \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B [/tex]

Obviously it can be solved by just creating a truth table and plugging in the four possibilities, but I was wondering whether it can be done without resorting to truth tables. In other words, can the expressions be simplified without plugging in values for A and B?

Please don't give me a complete solution, just tell me hint. I would like to figure this out on my own. I considered using De Morgan's Laws but I then had a feeling it would only complicate the expressions further.

All help is appreciated. Thanks!

BiP

I am trying to prove [tex] \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B [/tex]

Obviously it can be solved by just creating a truth table and plugging in the four possibilities, but I was wondering whether it can be done without resorting to truth tables. In other words, can the expressions be simplified without plugging in values for A and B?

Please don't give me a complete solution, just tell me hint. I would like to figure this out on my own. I considered using De Morgan's Laws but I then had a feeling it would only complicate the expressions further.

All help is appreciated. Thanks!

BiP