Solving Boolean Logic Expressions with And, Or and Not Gates

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The discussion revolves around identifying which of three boolean expressions involving two variables, A and B, are identical in their outputs across all combinations of True and False values. The expressions are: 1. (A and (not B)) or (B and (not A)) 2. (A and (not B)) and (B and (not A)) 3. (A or B) and (not (A and B))Participants suggest using truth tables to compare the outputs of the expressions, as this method clearly shows which expressions yield the same results. There is also mention of using boolean algebra to simplify the expressions for comparison. The original poster expresses confusion with using a simulator due to limitations in available gates, but ultimately finds clarity through the suggestions provided. The conversation emphasizes the importance of understanding boolean logic and the utility of truth tables in resolving such problems.
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The three equations below represent three different logic expressions using and, or and not gates of two boolean variables A and B. A boolean variable can take only one of two possible values: True or False.

Which of the two expressions are identical, meaning that for any combination of A and B they are both True or both False.

Expression 1: (A and (not B) ) or ( B and (not A))
Expression 2: (A and (not B)) and ( B and ( not A ))
Expression 3: (A or B ) and ( not ((A and B ))

In your answer explain how you figure out which expression is different (in terms of its output given the same combination of A, B and C) from the other two.

I tried to use the simulator to construct these, but since we don't have any combination gates on our program (NOR, NAND, etc.), I'm having a lot of trouble with it. We only have the AND, OR, and NOT gates to work with. Could someone please help me? I am really confused right now. Thank you.
 
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Expect it to be moved soon.

That aside, you could just construct truth tables and see which end up the same.

Or are you supposed to use boolean algebra to turn one of them into another?
 
I actually just figured this one out. Thank you for the pointer, though!
 

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