# 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)
$\begin{array}{ccc}
P & Q & {(P \downarrow Q)} \\ \hline
T & T & F \\
T & F & F \\
F & T & F \\
F & F & T \\ \end{array}$

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

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