1. ## 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.

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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 =/

2. 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 =/
Those are incorrect i'm afraid. Here's how to go about this

Let $\displaystyle P$ and $\displaystyle Q$ be statements.

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

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

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

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

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

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

3. 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)