Solving Boolean Logic Expressions with And, Or and Not Gates

[intellect]

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.

 

[Grep]

Homework questions need to be in this forum:

Science Education > Homework & Coursework Questions > Engineering, Comp Sci, & Technology

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?

 

[intellect]

I actually just figured this one out. Thank you for the pointer, though!