# Math Help - Logic question!

1. ## Logic question!

I'm doing my homework, and I try to do this problem but I got stuck. Please help, thank you so much

Here is the problem:
(p v ~r) ^ (~q)

a)1) simplify this one to the simplest form
2) find a way to write this one using a NAND instead of AND and OR if you do not remember the NAND its the (not AND ) or opposit of AND

2. ## Re: Logic question!

Hey Tiome.

Are you aware of the distributive laws involvings ^'s and v's (There are two depending on what's in the brackets)?

3. ## Re: Logic question!

Originally Posted by Tiome
Here is the problem:
(p v ~r) ^ (~q)

a)1) simplify this one to the simplest form
This depends on the meaning of "simple." If "the simplest" means "having as few connectives as possible," then this formula is already pretty much in the simplest form. You could also replace p \/ ~r with r -> p to reduce the number of connectives. If "the simplest" means that the formula is a disjunction of conjunctions of literals, then you need to use the distributive law, as chiro said.

Originally Posted by Tiome
2) find a way to write this one using a NAND instead of AND and OR if you do not remember the NAND its the (not AND ) or opposit of AND
One can express any Boolean function with just NAND. To see how to express the basic connectives, see here.