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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?

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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: $~~p\wedge q={{\neg p}}\star{{ q}~~~}$

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  • $\begingroup$ Thank you. Now I've seen the answer, I get it, but do you just have to spot it so to say? Is there a method to it? $\endgroup$ – the man May 28 '18 at 23:26

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