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I am reviewing for my upcoming Discrete Mathematics class and I'm clueless on the aforementioned question. I've tried expounding the XOR operator in hopes of transforming the problem but still I cannot find the solution to the problem.

The title is pretty self-explanatory, how do I prove their logical equivalence without using a truth table?

The truth table of the problem looks like this:

Problem truth table

enter image description here

StubbornAtom
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marshblocker
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1 Answers1

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XOR evaluates to true when there are "odd" number of true inputs. So the order and association don't matter. You may think of XOR as$\mod 2$ operator. As an example, $$odd + even +even = odd $$ It doesn't matter how you order or associate the inputs.

AgentS
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