PROJECT $2$ LOGIC

Objective: To use the ideas of logic to interpret a 'real

world' claim.

$$ You may work alone or with one or two other people from the class $($No more than

three people in a group$).$ If you work with other people, you will hand in one project

and each of you will receive the same grade, so be sure every member of the group

contributes equally to the project.

$$ When you submit the project, use only one side of each piece of paper. The project

should have a title sheet with the name of each person.

$$ If you hand in the project late, points will be deducted from your grade.

Method:

$1.$ Select one of the following that makes or implies a conditional statement. You should

have three variables and also include a conjunction or disjunction.

a$.$ an advertisement from a newspaper or magazine. $($Include a copy to your project.$)$

b$.$ an advertisement from TV or radio. $($Copy the claim exactly as you heard it$.)$

c$.$ a statement from a legal document or insurance policy. $($Include a copy with the

relevant section highlighted, or copy down the claim$)$

$2.$ Write the statement in symbolic form. Clearly state what each symbol represents.

$3.$ Create a truth table.

$4.$ Pick one row in your truth table where the final truth value is true.

a$.$ Translate the symbols back into English, using the truth values.

b$.$ Analyze whether this situation might happen, and under what conditions. Explain why

this situation might happen in real life.

$5.$ Pick one row in your truth table where the final truth value is false.

a$.$ Translate the symbols back into English, using the truth values.

b$.$ Analyze whether this situation might happen, and under what conditions. Explain why

this situation might happen in real life.

$6.$ Explain whether you think any of the possibilities that show the company lying. $($Where the

value under the conditional is false$)$ could actually happen.

$7.$ In your own opinion, is the company's claim true? Explain clearly.

EXAMPLE:

An advertisement in a magazine makes the following claim:

$"$If you use Sunshine Face Lotion, then your skin will be radiant and will have no

wrinkles."

a$.$ Translate the statement to the symbolic form.

p: you use Sunshine Face Lotion.

q: your skin will be radiant.

r: your skin will have wrinkles.

b$.$ Create a truth table.

p q r ~r q $^$ r p$->($q $^$ ~ r$)$

T t T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

c$.$ Pick one row in the truth table where the final truth value is true.

i$.$ For row $6,$ since p is false, q is true and r is false, then p$->($q $^$ ~ r$)$ is true.

ii$.$ Analyze whether the situation might happen, and under what condition.

Explain why this situation might happen in real life.

d$.$ Pick one row in the truth table where the final truth value is false.

i$.$ For row $4,$ since p is false, q is false and r is false, then p$->($q $^$ ~ r$)$ is false.

ii$.$ Analyze whether the situation might happen, and under what condition.

Explain why this situation might happen in real life