MTH 314 – Assignment 2
Due: 11:59pm, Sunday, January 21, 2024
(scan or take a photo of your solutions and upload to D2L)
1. (Exercise 44 in 2.2) Rewrite the statement
A sufficient condition for Jon’s team to win the championship is that it win the rest of its games.
in if-then form.
2. (Exercise 45 in 2.2) Rewrite the statement
A necessary condition for this computer program to be correct is that it not produce error messages
during translation.
in if-then form.
3. (Exercise 10 in 2.3) Use a truth table to determine whether the argument
p→r
q→r
∴ p∨q →r
is valid.
4. Use the truth-table to determine whether the following argument is valid:
(a) (p ∧ q) → ∼ r
(b) p∨ ∼ q
(c) ∼ q → p
(d) ∴ ∼ r
5. (Exercise 27 in 2.3) Use symbols to write the logical form of the argument
If this number is larger than 2, then its square is larger than 4.
This number is not larger than 2.
∴ The square of this number is not larger than 4.
If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, give an
example of truth values for p and q which show that the argument is invalid.
6. (Exercise 42 in 2.3) A set of premises and a conclusion are given. Use the valid argument forms listed
in Table 2.3.1 to deduce the conclusion from the premises, giving a reason for each step.
(a) p ∨ q
(b) q → r
(c) p ∧ s → t
(d) ∼ r
(e) ∼ q → u ∧ s
(f) ∴ t