# rewrite logical connectives in terms of not and and

so im supposed to rewrite $P\lor Q$, and , $P \Rightarrow Q , P \Leftrightarrow Q$ in terms of $\lnot$ and $\land$

this is what i got

$P \lor Q = ¬ P \land ¬ Q$

$P \land Q = P~Q$ (same thing?)

$P ⇒ Q = Q \lor ¬P$

$P ⇔ Q = ¬ P \land ¬Q$

those loook right?

The first three are right, the fourth should be: $$P \iff Q \equiv (P \land Q) \lor (\lnot P \land \lnot Q) \equiv \lnot (\lnot (P \land Q) \land \lnot (\lnot P \land \lnot Q))$$
2. yes, the same thing ($P\land Q$)
3. go further, use 1. to express it by $\land,\ \lnot$
4. not correct. use 3. and $P\Leftrightarrow Q = (P\Rightarrow Q)\land(Q\Rightarrow P)$