Need help with Boolean algebra

Find expressions for each of P$\displaystyle \vee$Q, P$\displaystyle \wedge$Q, and P$\displaystyle \rightarrow$Q that use only the

connective $\displaystyle \uparrow$ . (Your answers should not contain the symbol ¬.) In this case the up arrow is a NAND gate.

Not sure how to go about doing this one, any help would be appreciated.

Re: Need help with Boolean algebra

Note that $\displaystyle \neg P=P\uparrow P$, so $\displaystyle P\land Q=\neg(P\uparrow Q)=(P\uparrow Q)\uparrow(P\uparrow Q)$. Now you have negation and conjunction, from which you can express all other connectives.