contestada


Show that the following argument with hypotheses on lines 1–2 and conclusion on line c is
valid, by supplementing steps using the rules of inference and/or logical equivalences. Clearly label which rule you used in each step.

1. p → q
2. ∼ (q ∨ r)
c. ∼ p

Respuesta :

aramisdegaula1977

Answer:

Step-by-step explanation:

[tex] p \Rightarrow q \equiv (\neg p \vee q) [/tex] [logical equivalence]

[tex] \neg (q \vee r) \equiv (\neg q \wedge \neg r) [/tex] [morgan laws]

if [tex] (\neg q \wedge \neg r) [/tex] is true, then [tex] \neg q [/tex] is true and [tex] \neg r [/tex] is too.

with [tex] \neg q [/tex] true, then [tex] q [/tex] is false [double denial]

In the first equivalence it follows that [tex] \neg p [/tex] is true [identity law]

Then it can be concluded that [tex] \neg p [/tex]

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