Activity in SOUND and UNSOUND Argument
Determine if the argument is SOUND or UNSOUND by supplying what is asked in each of the following.
1. Argument: If I go to college (c), then I will not be able to work for my Dad (~𝑤). I did not go to
college. Therefore, I went to work for my Dad.
Write the following in symbols. Then supply the truth values in the table below that
corresponds to the column #.
(1) 1st Premise: 𝒄 → ~𝒘 (1pt)
(2) 2nd Premise: ~𝒄 (1pt)
(3) Conclusion: 𝒘 (1pt)
(4) Translate the argument into a conditional statement by combining the premises with ∧.
Please be careful in using of the grouping symbols. (3pts)
[(𝒄 → ~𝒘)∧ ~𝒄]→ 𝒘
Complete the truth table. (20pts)
c
w
~𝒘
(1)
(2)
(𝟏) ∧ (𝟐)
(4)
T
T
F
F
F
F
T
T
F
T
T
F
F
T
F
T
F
T
T
T
T
F
F
T
T
T
T
F
Hence, the argument is (Sound or Unsound?) Unsound. (3pts)
2. Argument: If I wake up early(𝑒), then I can attend my class on time (𝑎).If I attend my class on
time, then I can submit the activities on time (𝑠).I didn’t wake up early. Therefore, I couldn’t
submit the activities on time.
Write the following in symbols. Then supply the truth values in the table below that
corresponds to the column #.
(1) 1st Premise: 𝒆 → 𝒂 (1pt)
(2) 2nd Premise: 𝒂 → 𝒔 (1pt)
(3) 3rd Premise: ~𝒆 (1pt)
(4) Conclusion: ~𝒔 (1pt)
(5) Translate the argument into a conditional statement by combining the premises with ∧.
Please be careful in using of the grouping symbols. (3pts)
{[(𝒆 → 𝒂)∧(𝒂 → 𝒔)] ∧ ~𝒆} → ~𝒔
Complete the truth table. (56pts)
e
a
s
(1)
(2)
(3)
(4)
(𝟏) ∧ (𝟐)
[(𝟏) ∧ (𝟐)]∧ (𝟑)
(5)
T
T
T
T
T
F
F
T
F
T
T
T
F
T
F
F
T
F
F
T
T
F
T
F
T
F
F
F
F
T
T
F
F
F
T
F
T
F
F
T
F
T
T
T
T
T
F
T
T
F
F
T
F
T
F
T
T
F
F
T
F
F
T
T
T
T
F
T
T
F
F
F
F
T
T
T
T
T
T
T