Finding equivalent of $p\land q$ using only implication and $\bot$

Question

What is a formula equivalent of $p\land q$ that uses only $p$ and $q$, $\to$ and $\bot$ connectives?

$\to$ is so confusing... Could anyone help me out? Thanks in advance!

Answer 1

We have $$p\to q\equiv\neg p\lor q$$ By De Morgan's laws $$p\land q\equiv\neg(\neg p\lor\neg q)$$ We can express $\neg p$ as $p\to\bot$, so $$p\land q\equiv(p\to(q\to\bot))\to\bot$$