Question

"You cannot get on the airplane if you don't have a ticket unless you are the Pilot". Let a, b, and c represent "You can get on the airplane," "You have a ticket," and "You are an pilot," you can translate into a logical expression as.. a. (¬b∧¬c) -> (¬a) b. (¬a) -> (¬b ∧ ¬c) c. (b ∧ ¬c) ->(¬a) d. (¬a) ->(¬b ∧c)

Answer 1

Answer: [b   ¬c ]   a

Explanation:

Given

a: You can get on the airplane

b: You have a ticket

c: You are an pilot

Given Statement:

You cannot get on the airplane if you don't have a ticket unless you are the Pilot".

Proposition Form: (¬a)   (¬c ¬b )

Unless is used to represent " if not" Connective. i.e A Unless B = ¬B A

if is used to represent the Impies (  ) Connective

Given Proposition Form is (¬a)   (¬c ¬b )

(¬a)   [¬(¬c) V ¬b ]    { Law of Implies (PQ) = ¬PVQ }

(¬a)   [c V ¬b ]  {By De Morgan's law ¬ (¬P) = P }

(¬a)   [¬b V c ]  {Commutative law (P V Q) = (Q V P)}

(¬a)   ¬[b   ¬c ]  {By De Morgan's law ¬ (P V Q) = ¬P ¬Q }

¬(¬a) V ¬[b   ¬c ]   { Law of Implies (PQ) = ¬PVQ }

a V ¬[b   ¬c ]   {By De Morgan's law ¬ (¬P) = P }

[b   ¬c ]   a { Law of Implies ¬PVQ = (PQ) }

[b   ¬c ]   a