Boolean Expression Simplification: Z = P.Q.R + P.R

[Bazinga1c4x]

I have been trying to figure out how to apply the Boolean algebra laws to simplify questions like these below:

Z = P.Q.R + P.R
= Q.P+R (Commutative Law, idempotent Law)
= Q.P+Q.R Distributive Law


z=A.B.C+A.B.C+A.B.~C+A.B.C

I have no clue if what I had done above is correct or not and am really lost and confused, I would appreciate it if someone could answer the example and explain how they did it thank you.

 

[stapel]

I have been trying to figure out how to apply the Boolean algebra laws to simplify questions like these below:

Z = P.Q.R + P.R
= Q.P+R (Commutative Law, idempotent Law)
= Q.P+Q.R Distributive Law


z=A.B.C+A.B.C+A.B.~C+A.B.C

I have no clue if what I had done above is correct or not...

What was the original exercise? What were its instructions? What does your book mean by the decimal-point notation? Does the tilde (the "~" character) mean "set complement"? How does your last equation relate to what came before? Or is it a second exercise?

Thank you!