I'm currently stuck on this question:
"Henry never wears his jacket and tie together at the same time. I.e. when Henry is dressed, he either doesn't wear his jacket, or he doesn't wear his tie, (or neither of the two items)."
Formalize the reasoning as a statement logic sequence by using the following variables:
- $k$: "Henry wears his jacket."
- $f$: "Henry wears his tie."
Prove the sequence using natural deduction.
I think the sequence would look like this: $$\vdash \neg(k \land f)$$ But how do I prove this? Is it even possible without any premises?
Since the exercise claims that it is specifying some reasoning instead of merely a claim, then I agree with Ten O'Four that the best guess is that they must be specifying an argument of the form "Conclusion, since Premise." (However, it is technically incorrect to interpret ‘I.e.,’—which starts the second sentence and is read “that is”—as “since”.)
Premise: when Henry is dressed, he either doesn't wear his jacket, or he doesn't wear his tie, (or he wears neither of the two items).
$$(\lnot k \land f) \lor (\lnot k \land \lnot f) \lor (k\land \lnot f) $$
Conclusion: Henry never wears his jacket and tie together at the same time.
$$\neg(k \land f)$$
Argue using disributive laws.