Download Homework #3 - Jonathan Livengood

PHIL 103: Logic and Reasoning QRII
Homework #3
Due Monday, September 23
1. Translate the following argument into our formal language and then use truth tables to
determine whether the argument is valid or invalid.
If the TV remote isn’t working, then John has to change channels manually.
John has to change channels manually.
The TV remote isn’t working.
2. Translate the following argument into our formal language and then use truth tables to
determine whether the argument is valid or invalid.
Totoro is a magical creature, and Totoro rides on a cat bus.
Totoro carries an umbrella.
Totoro carries an umbrella, and Totoro rides on a cat bus.
3. Use truth tables to show that the rule of conjunction elimination is valid. You may use
ordinary sentence letters instead of φ and ψ.
4. Use truth tables to show that the rule of arrow introduction is valid. You may use ordinary
sentence letters instead of φ and ψ.
5. Use truth tables to show that the rule of negation elimination is valid. You may use ordinary
sentence letters instead of φ and ψ.
6. Show the following: { (P ∧ Q), (P → R), ((Q ∧ R) → S ) } ⊢ S.
7. Show the following: { (~P ∨ Q), (~P → Q), (Q → Q) } ⊢ Q
8. Show the following: { (P → ~~Q), P } ⊢ Q.
9. Show the following: { P, Q, ((P ∧ (Q ∨ R)) → (S ∧ T )) } ⊢ T.
10. Translate the following argument and then give a formal proof of its conclusion from its
premisses.
Suzy throws a rock only if Billy throws a rock.
If Suzy does not throw a rock, then Suzy throws a stick.
Billy does not throw a rock.
Suzy throws a stick.