Discrete Structures Test 1
Question 1. (10 points) Use a truth table to show that the following wff is a tautology.
Question 2. (12 points) Let A, B, and C be the following statements:
A: I am thirsty.
B: My glass is empty.
C: It is three o'clock.
Translate the following compound statements into propositional well-formed formulas.
a) I am thirsty and my glass is not empty.
b) It is three o'clock and I am thirsty.
c) If it is three o'clock, then I am thirsty.
d) If I am not thirsty, then my glass is not empty.
Question 3. (13 points) Prove the following wff with propositional logic.
Question 4. (15 points) Give an interpretation to prove that the following wff is not valid.
Question 5. (20 points) Prove the following wff using predicate logic.
Question 6. Consider the following verbal argument.
Every pig is smarter than every horse. Arnold is a pig. But there is an owl and Arnold is not smarter than that owl. Therefore, something is not a horse.
a) (15 points) Translate the following verbal argument into a predicate logic wff. Use the predicate symbols:
P(x): x is a pig
H(x): x is a horse
O(x): x is an owl
S(x, y): x is smarter than y
b) (15 points) Use predicate logic to prove the above argument.