# How can I write a constructive adhoc argument for proofs?

In Discrete Mathematics we are being asked to write adhoc arguments. At times I get quite confused (i'm a rookie) when it comes to writing these to prove a certain statement is true.

i.e. Prove (p^q) -> (pv not r) is a tautology.

What is the ideal way to write an adhoc argument to prove a statement as such?

• What do you mean by "adhoc argument"? – mrp Aug 4 '17 at 7:03
• From my understanding it's just justifying why the statement is true. – Oliver K Aug 4 '17 at 7:09
• That's what I would call a proof, so what is the difference between adhoc arguments and proofs? – mrp Aug 4 '17 at 10:09

## 1 Answer

Are you using truth table? If yes, then you need to prove that $p \land q \to p \lor \neg r$ is 1 ever. But, using what we know about implication, it is 0 iff $p \land q = 1$ and $p \lor \neg r = 0$, but, if $p \land q = 1$, then $p =1$ and $q = 1$ and therefore $p \lor \neg r = 1$.

Maybe you are using a calculus, in this case, what system are you using? In natural deduction, you eliminate the implication, get $p \land q$ and use $p \land q$ to prove $p$ and after use $p$ to prove $p \lor \neg r$.

As you say tautology, must be truth table.