Math Help - Need help with Boolean algebra

1. Need help with Boolean algebra

Find expressions for each of P $\vee$Q, P $\wedge$Q, and P $\rightarrow$Q that use only the
connective $\uparrow$ . (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.

2. Re: Need help with Boolean algebra

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