Geometry / Mr. Hansen 9/16/2003

Name: _________________________

Conditional Statements Worksheet

Part I.	Instructions: Read each of the following arguments, assume that the given statements are true, and state whether the conclusion is valid. If it is not, explain the error in the reasoning.
1.	Given:    Koala Bears eat nothing but eucalyptus leaves.    Yesterday there were leaves on my eucalyptus tree, but today there are none. Conclusion: A koala bear ate the leaves off my eucalyptus tree.
2.	Given:    You must pay a fine of $50 only if your dog does not have a license.    Your dog does not have a license. Conclusion: You must pay a fine of $50.
3.	Given:    I know the correct phone number if I have reached the party to whom I am speaking.    I have reached the party to whom I am speaking. Conclusion: I know the correct phone number.
Part II.	Brain Teaser! Problems 4 and 5 are equivalent, but #5 is probably easier.
4.	Each of four notecards has a single letter written on one side of the card and a single digit number written on the other side. Suppose that these four cards are on a table in front of you, as shown below, and you are required to establish the truth of a conditional statement by turning over exactly two of the cards. Which two cards should you turn over to decide whether the following statement is true or false? “If the letter A is on one side of the card, then the number 3 is on the other side.”
5.	It is the year 2011, and you are working as a bouncer at a restaurant. Your job is to keep underage customers from drinking alcohol. (In other words, you want to make sure that the implication “alcohol Þ age ³ 21” is always true.) A co-worker comes to you and tells you that there are four people upstairs. Each person has one beverage, but on a quick pass it was not possible to get complete information. Here is what we do know: Person #1 is drinking beer. Person #2 is drinking ginger ale. Person #3 is an elderly gray-haired gentleman walking with the aid of a cane. Person #4 is a Beauvoir student. (This is not a trick question. For example, the gray-haired man is really old, not simply pretending to be old. The beer and ginger ale are genuine, and the Beauvoir student is of a typical age, not someone who was held back for 13 years.) Of these four customers, which one(s) should be checked more closely?