Math 2534 Homework 1:
Problem 1:
Let p, q and r be the propositions given below:
p: Grizzly bears have been seen in the area.
q: Hiking is safe on the trail.
r: Berries are ripe along the trail.
Put the sentences below into symbolic logic notation.
a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.
b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries
are ripe along the trail.
c) Grizzly bears have been seen in the area or the berries are not ripe.
Problem 2: For each of the sentences below, determine whether an ‘exclusive or’ or an
‘inclusive or’ is intended.
1) Lunch includes soup or salad in the price.
2) Experience in C++ or Java is required.
3) When you buy a new car from Acme Motor Company, you get $2000 back in cash or
2% in car loan.
4) School is closed for more than 8 inches of snow or if the wind chill is 8º.
Problem 3:
Construct a truth table to verify the following equivalence relations:
1) p ∨ (q ∧ r ) ≡ ( p ∨ q ) ∧ ( p ∨ r ) (Distributive Law)
2) ∼ ( p ∨ q) ≡∼ p ∧ ∼ q (DeMorgan's Law)
3) p ∧ ( p ∨ q) ≡ p (Absorption Law)