Answer to Question #313312 in Discrete Mathematics for pauljohn

Question

1. Let p and q be the propositions. (50 points)

p: It is below freezing.

q: It is snowing.

Express each of these propositions in complete English sentences.

a) p ∧ q (7 points)

b) p ∧ ¬q (7 points)

c) ¬p ∧ ¬q (7 points)

d) q ∨ p (7 points)

e) p → q (7 points)

f) q ∧ ¬p (7 points)

g) q → p (8 points)

 

2. Solve the following. (50 points)

a) Construct a truth table. (10 points)

¬p ∧ ( p ↔ ¬q )

b) Construct a truth table. (10 points)

p → ( q ∧ r )

c) Construct a truth table. (10 points)

( p → q ) ∨ ( ¬p ↔ r )

d) Find out if the following is a tautology, contradiction, or contingency. (10 points)

( p ∨ q ) ∧ ( ¬p ∧ ¬q )

e) Find out if the following propositions have logical equivalence. (10 points)

( p ↔ q ) ≡ ( p → q ) ∧ ( q → p )