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verification problem

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bogla

New Member
Here is a problem I'm trying to solve.






Here is the given solution in my book.




I don't understand that marked area in the solution.

Need help to understand it to move ahead.

Can anybody please explain that in a simpler way?

Thanks
 

MikeMl

Well-Known Member
Most Helpful Member
Let me try to restate the problem:

1. By definition, A*B=AB + !A!B, where !=not (the * operator is sorta like ex-or)

2. Let C=A*B

3. Verify that A=B*C

4. Substitute A*B for C in the above equation, A=B*A*B, but also put () around the last two terms, so it looks like this: A=B*(A*B)

5. Now use the definition of the connective operator (equ 1) to expand equ 4: A=!B!(A*B) + B(A*B)


ps 50 years as a logic designer, and I never heard of the "connective"
 

bogla

New Member
5. Now use the definition of the connective operator (equ 1) to expand equ 4: A=!B!(A*B) + B(A*B)
awesome. got this part.

But stuck in the next step here.

Please see this step.

Is it a law ? which law ? or how can we do that step there ?
 

MikeMl

Well-Known Member
Most Helpful Member
That transition can be shown with a simple two-term, four-square Veich diagram, aka DeMorgan's Theorem
 
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