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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?

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

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