# Arguments

Please take approximately 1 hour to answer the following questions. Submit as a pdf under the “Arguments” assignment on Blackboard. Read the instructions for each question carefully.

1. (8 pts) Select a (well known) song that you think is making an argument. Paste the song title, artist, and lyrics below. Write 5 underlying mathematical statements that the song is making. Even if the song is making statements that are not quite mathematical, you should extrapolate mathematical statements. These statements can be direct from the song or subtext from the song. At least 2 of the statements should be conditional statements.

Write the contrapositive of two of the conditional statements listed above.

What assumptions/premises is the songwriter making in their argument? (at least 3)

What is the ultimate conclusion being drawn?

• (3 pts) Find a news article that you believe involves a logical fallacy that we discussed in class (besides ad hominem). Explain the argument and the underlying fallacy. Give a link to the article you found.
• (3 pts) What are your strengths and weaknesses as a problem solver? What steps could you take to improve?
• (3 pts) In class we talked about the error people tend to make of “assuming the converse.” Describe a scenario where you have wrongly assumed the converse of a true statement to be true.
• (3 pts)

Joe recently went to the famed Wit-fil-a restaurant. He saw a sign by their play place that read, “If you are more than 48 inches tall, then you may not play in the play place.” He looked down at his 40 inch tall 4-year-old son, Beau, who was not playing in the play place. A nearby woman,  Dorian, also saw the sign and looked at her 36 inch tall daughter, Parker, who was in the play place. Joe and Dorian each believe they have observed scenarios that prove the rule has been broken. They complain to the Wit-fil-a staff. The staff say that the sign is still true. Joe and Dorian decide to sue Wit-fil-a for false advertising. Their case was thrown out in court. The sign was deemed truthful, enforceable, and legally binding.

1. What concept from our class did both Joe and Dorian fail to comprehend? (Note, Joe and Dorian both act illogically on many levels here, but one particular concept is blatantly misunderstood by both of them).
• Does the sign explicitly say anything about whether or not Beau and Parker are allowed to play in the play place?  (If Parker just dumped a lemonade all over herself, does Wit-fil-a still have to allow her to play in the play place since she is not over 48 inches tall?)
• (5 points) Use a truth table to determine whether the following argument is valid or invalid:

If it rains then the game will be cancelled. Either the game is not canceled or the concession stand is closed. It rained. Therefore the concession stand is closed.

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