[Math] Rules of inference: The Rules of Disjunctive Syllogism and Double Negation

Question

I have a question about the use of Double Negation in relation to this problem I found in my textbook examples.

Problem:

1. $\;¬(r \land t) \lor u$
2. $\;r \land t$

Therefore, $u$.

In my textbook it says it used the double negation and then followed by the Rule of Disjunctive Syllogism. I understand that we have to turn premises 1 and 2 into premises that can be used with disjunctive syllogism, but I don't know the STEPS taken using double negation to get it into the form to be used with disjunctive syllogism. Help is much needed! I really can't figure out how double negation was employed here.

Answer 1

1. $\;\lnot (r \land t)\lor u,\;$ (premise)

2. $\;r\land t,\;$ (premise)

$\lnot \lnot (r \land t)$ from $(2),\;$ (double negation)

$\therefore \;u\;$ (disjunctive syllogism)