# Truth Tables

• Mar 17th 2014, 05:39 PM
Gayelle
Truth Tables
Are these two statements equivalent?

When I simplify “not (not p and q) or (p and not r)” via rules I get “p or not q”.
However the truth tables don’t seem to add up.

Not (not p and q) or (p and not r)

p q r not (not p and q) or (p and not r)

1 1 1 1
1 1 0 1
1 0 1 1
1 0 0 1
0 1 1 0
0 1 0 0
0 0 1 1
0 0 0 1

p or not q

p q p or not q
1 1 1
1 0 1
0 1 0
0 0 1

Thanks
• Mar 17th 2014, 05:47 PM
SlipEternal
Re: Truth Tables
Where do the parentheses go? From what I see, Not(not p or q) or (p and not r) simplifies (to me) to:

(p and not q) or (p and not r)

Which then simplifies to

p and (not q or not r)

Then:

p and not (q and r)

So, I don't see how you simplified to "p or not q".
• Mar 17th 2014, 06:03 PM
Gayelle
Re: Truth Tables
Quote:

Originally Posted by SlipEternal
Where do the parentheses go? From what I see, Not(not p or q) or (p and not r) simplifies (to me) to:

(p and not q) or (p and not r)

Which then simplifies to

p and (not q or not r)

Then:

p and not (q and r)

So, I don't see how you simplified to "p or not q".

It was supposed to be "Not (not p and q) or (p and not r)".

Sorry I'm not used to this.
• Mar 17th 2014, 06:12 PM
SlipEternal
Re: Truth Tables
$\begin{matrix}p & q & r & \neg(\neg p \wedge q)\vee(p\wedge \neg r) & p\vee \neg q \\ -- & -- & -- & --------- & ---- \\ T & T & T & T & T \\ T & T & F & T & T \\ T & F & T & T & T \\ T & F & F & T & T \\ F & T & T & F & F \\ F & T & F & F & F \\ F & F & T & T & T \\ F & F & F & T & T\end{matrix}$

They look equivalent to me.
• Mar 17th 2014, 06:19 PM
Gayelle
Re: Truth Tables
Ok got it.

Thanks!