verification problem

[bogla]

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]

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]

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]

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

 

[Ratchit]

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

Don't knock yourself out trying to help this multiple poster. Different userid, but same individual. https://www.electronicspoint.com/threads/validity-of-equation.288416/

Ratch