Select an advertisement from the Internet, a newspaper, or a magazine that makes or implies a conditional statement. Analyze the advertisement to determine whether the consequent necessarily follows from the antecedent. Explain your answer. (See Example.)
Example
Examining an Advertisement
An advertisement for Perky Morning coffee makes the following claim: “If you drink Perky Morning coffee, then you will not be sluggish and you will have a great day.” Translate the statement into symbolic form and construct a truth table.
Solution Let
p: You drink Perky Morning coffee.
q: You will be sluggish.
r: You will have a great day.
In symbolic form, the claim is
P→(~q ∧ r)
This symbolic statement is identical to the statement in Table, and the truth tables are the same. Column 3 represents the truth values of (~q ∧ r), which corresponds to the statement “You will not be sluggish and you will have a great day.” Note that column 3 is true in cases (rows) 3 and 7. In case 3, since p is true, you drank Perky Morning coffee. In case 7, however, since p is false, you did not drink Perky Morning coffee. From this information we can conclude that it is possible for you to not be sluggish and for you to have a great day without drinking Perky Morning coffee.
p | 1 | T | P |
| (~q |
| A | r) |
T | T | T | T | F | F |
| F | T |
T | T | F | T | F | F |
| F | F |
T | F | T | T | T | T |
| T | T |
T | F | F | T | F | T |
| F | F |
F | T | T | F | T | F |
| F | T |
F | T | F | F | T | F |
| F | F |
|
|
|
|
|
|
|
|
|
F | F | T | F | T | T |
| T | T |
F | F | F | F | T | T |
| F | F |
4 |
|
|
| 5 | 1 |
| 3 | 2 |
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