P310 Valid Reasoning II
Professor: Craig DeLancey
Office: Marano 212A
Last two track homework! Do problem 1 and 3 or problem 2 and 3.
1. Read chapters 11-16 of A
Concise Introduction to Logic. Do problems:
- Chapter 11, problems 1a, 1b, 1c, 2b, 2c.
- Chapter 12, problem 2
- Chapter 13, problems 1a, 1e
- Chapter 14, problems 1a, 1b
It turns out that we can say everything that
can be said in the propositional logic using
just two connectives: ¬ and →.
Prove this by making expressions equivalent
to (P v Q) and (P ^ Q) and (P ↔ Q) that
use only negation and conditionals. Make truth
tables to show that your expressions have the
same meaning as the disjunction, conjunction, or
3. Prove the following theorems.
- (∃x∀yFxy → ∀y∃xFxy)
- (∀x∃y(Fx → ∃z(Gz → Hy))
→ ((∃xFx ^ ∀xGx) → ∃xHx))