Homework III
Logic and Discrete Mathematics
Deadline September 22, 2016
1. Show that (p → q) ∨ (p → r) and p → (q ∨ r) are logically equivalent. Try the sequent
calculus inference rules.
2. Show that (p ∨ q) ∧ (p ∨ r) → (q ∨ r) is a tautology.
3. Determine the truth values of the statements ∀x∃y(xy = 1) and ∃x∀y(x 6 y 2 ) if the
domain for the variables consists of
a) the nonzero real numbers;
b) the nonzero integers;
c) the positive real numbers.