# Thread: Expressing propositions using a defined connective.

1. ## Expressing propositions using a defined connective.

Hello!
I need a help with some problem of discrete mathematics.

Can someone help me to solve this problem :

"We define the connective( / )by:
P/Q = not(P or Q)
Show that all proposition composed of P and Q can be only expressed thanks to this connective ( / )"

2. Originally Posted by Crissman
"We define the connective( / )by:
P/Q = not(P or Q)
Show that all proposition composed of P and Q can be only expressed thanks to this connective ( / )"
It is useful to have the truth table for the ‘dagger connective’ (joint denial)
$\displaystyle \begin{array}{ccc} P & Q & {(P \downarrow Q)} \\ \hline T & T & F \\ T & F & F \\ F & T & F \\ F & F & T \\ \end{array}$

I will give you the equivalent statements. But you must prove them.
$\displaystyle \begin{array}{ccc} {\neg P} & \equiv & {P \downarrow P} \\ {P \wedge Q} & \equiv & {(P \downarrow P) \downarrow (Q \downarrow Q)} \\ {P \vee Q} & \equiv & {(P \downarrow Q) \downarrow (Q \downarrow Q)} \\ {P \to Q} & \equiv & {\left[ {\left( {P \downarrow P} \right) \downarrow Q} \right] \downarrow \left[ {\left( {P \downarrow P} \right) \downarrow Q} \right]} \\ \end{array}$

3. Thank you very much, you help me a lotttt