# Boolean logic expansion issue (POS -> CPOS)

1. May 27, 2014

### QuarkCharmer

1. The problem statement, all variables and given/known data
Convert f=(x'+y)(x+z)(y+z) from product of sums form, into the canonical product of sums.

2. Relevant equations
boolean logic, et al.

3. The attempt at a solution

This is boolean logic (so + is "or" and * is "and" etc..)

There has to be some stupidly simple thing I am overlooking here. I chose to break it down and work each Maxterm by itself.

So the first thing to expand is:
(x'+y)
and so:
(x'+y) = x' + y + zz' since zz' = 0 this is okay.

Now here is the part I am not following.

I know that x' + y + zz' = (x' + y + z)(x' + y + z')

but I don't know how this expansion is happening.

2. May 27, 2014

### verty

This is just the distribution rule: $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$.

PS. Learn the rules by heart, there aren't too many of them.

3. May 27, 2014

### QuarkCharmer

oh god your right.

Thanks.

I should have just wrote it out without all the + and * nonsense and I would have seen that.

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