Boolean Algebra Simplification Property Question

[Bigworldjust]

Hi I am not sure where to post this question but I am trying to simplify this expression:

r*c'w+c (As in R AND NOT C AND W OR C) to c+wr (As in C OR W AND R) and I know that it simplifies to this and they are both equivalent; however my question is which boolean simplification property is used here? Is it the Absorption principle? Thank you!

 

[MisterX]

No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?

 

[Bigworldjust]

No, I don't think so. It follows from the distributive property of OR over AND, combined with the compementation principle x OR x' = 1.

Is this homework?

No it's a worked example left for us to solve if we wanted extra practice. And that's what I thought initially. So it is using the distributive property and then the complement theory. Thank you.

 

[Bigworldjust]

Also one last question. When expressions are functionally equivalent like the two above, can they always be reduced to being identical? I am assuming yes, because they are equal to begin with, correct?

 

[MisterX]

Two Boolean expressions that have the same variables are equal if and only if they have identical truth tables.