# Propositional

• Sep 13th 2007, 03:56 PM
greensnake
Propositional
a propositional p is given with p :If christmas lasts to easter, I get more presents.

a) Form the negation to the propositional p

b) Form the contrapositive form to the propositional.

________________________________________________

a) If christmas won't last to easter, I won't get more presents ..

b) Christmas lasts to easter, so I will get more presents..

Is anyone of that even slightly right, I missed a few classes so I don't know that much sadly =/
• Sep 13th 2007, 04:10 PM
Jhevon
Quote:

Originally Posted by greensnake
a propositional p is given with p :If christmas lasts to easter, I get more presents.

a) Form the negation to the propositional p

b) Form the contrapositive form to the propositional.

________________________________________________

a) If christmas won't last to easter, I won't get more presents ..

b) Christmas lasts to easter, so I will get more presents..

Is anyone of that even slightly right, I missed a few classes so I don't know that much sadly =/

Let $P$ and $Q$ be statements.

We call the statement: "If $P$, then $Q$" an "implication," and often write it as shorthand using the following logical symbols: " $P \implies Q$"

The contrapositive of $P \implies Q$ is $( \neg Q) \implies ( \neg P)$

When we are negating an implication, we use the fact that:

$P \implies Q \equiv ( \neg P) \vee Q$

So the negation of $P \implies Q$ is $\neg (P \implies Q) = \neg ( ( \neg P) \vee Q) \equiv P \wedge ( \neg Q)$ by DeMorgan's Laws.

Note: the $\neg$ symbol means "not." So, for instance, $\neg P$ means "not P"

you may want to see here, they don't have symbols, but the explanations are ok.

Now, do you think you can continue?
• Sep 13th 2007, 04:44 PM
greensnake
Ok, I think I got some of it.

So,

a) Christmas lasts to easter, I won't get any more presents.

b) I won't get anymore presents, so Christmas won't last to easter.

I think b) is right, but not too sure about a) (negation)