January 16
Name:
Choose the best answer to each of the following questions. Explain your reasoning with one or more
complete sentences.
1. 3pts Suppose that A represents the set of all whole numbers and B represents the set of all irrational
numbers. The correct Venn diagram for the relationship between these sets is
b. The sets A and B are disjoint, no whole numbers are irrational.
2. 3pts Suppose that A represents the set of all people above the age of 10 and B represents the set
of a U.S. registered voters. The correct Venn diagram for the relationship between these sets is
The best answer is c. Some people above the age of 10 are voters.
3. 3pts In the Venn diagram below, the X tells us that
c. some women are not veteranians. This region is outside the set of veteranians and inside the set
of women.
4. 3pts To prove a statement is true, you must use
b. a deductive argument. Elimate the other choices: inductive arguments have various subject
strength, while conditional propositions require more information about the premises.
5. 3pts A deductive argument cannot be
c. sound but not valid. Sound deductive arguments require valid logic.
6. 3pts Consider an argument in which Premise 1 is ”All fruit is fat-free” and Premise 2 is ”Avocados
are fruit.” If X represents avocados, which Venn diagram correctly represents the two premises?
c. Premise 1 indicates the set of fruit is a subset of fat free foods, while premise 2 indicates avocados
are members of fruit.
7. 4pts For the given categorical proposition, do the following.
a. State the subject set and predicate sets.
b. Draw a Venn diagram for the proposition and label all regions of the diagram.
”Every child can sing.”
a. S = set of children. P = set of singers. b. The Venn diagram for this is that S is a subset of P
(much like picture c for problem 6.
8. 4pts Use the Venn diagram to answer the following questions.
a. How many men at the party are over 30 ?
b. How many women are at the party?
a. The number we want is outside the set of women, and outside the set of people under the age of
thirty, which is the number 20. b. The sum of the numbers inside the set of women is 16 + 8 = 24.
9. 4pts Is the following deductive argument valid or not, and is it sound or not?
Premise: All U.S. presidents are men.
Premise: George Washington was a man.
Conclusion: George Washington was a U.S. president.
This is not a valid argument. The set of US presidents is a subset of the set of men, but the premises
would place an X on the edge of the set of US presidents. This is not inside the Venn diagram for
the conclusion. The premises are true, but the argument is not valid, so it is also not sound.