Question

Use propositional logic to prove the following argument is valid. If Alice gets the office position and works hard, then she will get a bonus. If she gets a bonus, then she will go on a trip. She did not go on a trip. Therefore, either she did not get the office position or she did not work hard or she was late too many times.
a) Define your propositions [5 points]: O = W = B = T = L =

b) Write down the logical argument [8 points]:

c) Proof sequence [12 points]: Steps: Reason: 1. 2. 3. …

Answer 1

Answer:

a). Define your propositions [5 points]:

O =  Alice Gets the Office position

W =  Alice Works Hard

B =  Alice Gets a Bonus

T =  Alice Goes on a Trip

L = Alice Was not Late

b).

((O ∧ W → B) → T)  ¬T(¬O ⊕ ¬W ⊕ ¬L)