Download Assignment : Logic and Proofs Exercise 1

Assignment : Logic and Proofs
Exercise 1:
Formulate each of the following symbolic expressions in words and determine its truth value knowing that
p is False, and q is True.
p: Lee takes computer science
q: Lee takes mathematics
r: Lee likes computer science
1.
¬p ∧ q
2.
p ∨ ¬q
3.
¬(p ∧ ¬ q)Æ r
4.
r ∨ p ↔ ¬q
Exercise 2 :
Write the following proposition symbolically:
If an animal is a rodent then its gnaws their food and is a mammal
Find the Truth Table:
a.
Find its converse and its contrapositive:
Converse:
Contrapositive:
Exercise 3: Write the following argument symbolically and use a truth table to determine if it is valid:
Hypotheses: if I play hockey, then I am sore the next day. I use the whirlpool if I am sore. I did not use the
whirlpool. Therefore I play hockey.
Truth Table:
Assignment : Logic and Proofs
Exercise 4 :
Let L(x, y) be the propositional function “x can fool y”. The domain of discourse is the set of all living
people.
Write each statement symbolically:
- Someone can fool everybody:
- No one can fool himself
Exercise 5 (15 pts):
Determine the truth value of each of the statements and justify your answer by providing a proof or a
counter example. The domain of discourse is the set of real numbers.
1.
For every x, x2 >x
2.
For some x, for some y, x2 + y2 ≥ 9