2. In this exercise we will explore the process of using a truth table to show that an argument is valid. (a) Let p be the statement "I will buy a skateboard." Let q be the statement "I will buy a scooter." Write the following argument in symbolic form. I will buy a skateboard, or I will buy a scooter I will not buy a skateboard. Therefore, I will buy a scooter. (b) Consider the symbolic pattern for the argument from (a). (An argument that follows this pattern is known classically as a disjunctive syllogism.) (1) Complete this truth table, which shows that the argument is valid. pvq T (pvq)^-p F P T T F F 9 T F T F T T -P F F F F T T (2) Explain why this truth table shows that the argument is valid. (c) Consider the following argument. p→q (1) Complete this truth table to show that the argument is not valid. 오 -P (pq)^-p F T F F F T F pvq T T If it snows, then I get cold. It does not snow. Therefore, I do not get cold. p→q T 9 (2) Explain why the truth table shows that the argument is not valid. (d) Use your work in (c) to help you evaluate the validity of the following argument. Explain your thinking carefully.
2. In this exercise we will explore the process of using a truth table to show that an argument is valid. (a) Let p be the statement "I will buy a skateboard." Let q be the statement "I will buy a scooter." Write the following argument in symbolic form. I will buy a skateboard, or I will buy a scooter I will not buy a skateboard. Therefore, I will buy a scooter. (b) Consider the symbolic pattern for the argument from (a). (An argument that follows this pattern is known classically as a disjunctive syllogism.) (1) Complete this truth table, which shows that the argument is valid. pvq T (pvq)^-p F P T T F F 9 T F T F T T -P F F F F T T (2) Explain why this truth table shows that the argument is valid. (c) Consider the following argument. p→q (1) Complete this truth table to show that the argument is not valid. 오 -P (pq)^-p F T F F F T F pvq T T If it snows, then I get cold. It does not snow. Therefore, I do not get cold. p→q T 9 (2) Explain why the truth table shows that the argument is not valid. (d) Use your work in (c) to help you evaluate the validity of the following argument. Explain your thinking carefully.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. In this exercise we will explore the process of using a truth table to show that an argument is valid.
(a) Let p be the statement "I will buy a skateboard." Let q be the statement "I will buy a scooter."
Write the following argument in symbolic form.
I will buy a skateboard, or I will buy a scooter
I will not buy a skateboard.
Therefore, I will buy a scooter.
(b) Consider the symbolic pattern for the argument from (a). (An argument that follows this pattern is
known classically as a disjunctive syllogism.)
(1) Complete this truth table, which shows that the argument is valid.
pvq
T
(pvq)^~p
F
P
T
T
F
F
T
F
T
F
P
T
T
F
F
(2) Explain why this truth table shows that the argument is valid.
(c) Consider the following argument.
P→q
-P
-P
F
F
T
T
(1) Complete this truth table to show that the argument is not valid.
(p→→q)^~p
F
9
T
F
T
F
pvq
-P
F
F
T
T
If it snows, then I get cold.
It does not snow.
Therefore, I do not get cold.
pq
T
9
(2) Explain why the truth table shows that the argument is not valid.
(d) Use your work in (c) to help you evaluate the validity of the following argument. Explain your
thinking carefully.
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