Propositional connective adequate

Question

Let $\star$ be a propositional connective that has the following truth table; \begin{array}{c|c|c} p & q & p \star q\\ T & T & F\\ T & F & F \\ F & T & T \\ F & F & F\\ \end{array}

I want to construct terms which are logically equivalent to $p \lor q$ and $ p \land q$ using only the connectives $\neg$ and $\star$.

How do I do this? I can see that $p \star q \equiv \neg p \land q$, thus $\neg (p \star q) \equiv p \lor \neg q $, but this isn't what I need?

Answer 1

You can see that $~\neg p\wedge q = ~~~p\star q~$ but actually want to find $p\wedge q$.

Can you see what $~~p\wedge q=\underline{\phantom{\neg p}}\star\underline{\phantom{ q}~~~}$?

Do you not see: $~~p\wedge q={{\neg p}}\star{{ q}~~~}$