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MTH 215 Week 5 Study Plan for Final Examination

• 1.C Sets and Venn Diagrams

• Use Venn diagrams with two sets.

• 1.C Sets and Venn Diagrams

• Use Venn diagrams with three sets.
• Use Venn diagrams with more than three sets.

• 1.D Analyzing Arguments

• Decide if a statement involving analyzing arguments makes sense.
• Decide whether an argument is deductive or inductive.
• Analyze inductive arguments.
• Analyze deductive arguments.

• 1.E Critical Thinking in Everyday Life

• Decide if a statement involving critical thinking in everyday life makes sense.
• Use critical thinking.
• Identify hidden assumptions or unstated issues.

• 4.B The Power of Compounding

• Decide if a statement involving interest makes sense.
• Calculate simple and compound interest.
• Find the annual percentage yield (APY).
• Calculate continuous compound interest.
• Find the present value, compare yields, and find time periods.

• 9.A Functions: The Building Blocks of Mathematical Models

• Decide if a statement involving mathematical models makes sense.

• 9.C Exponential Modeling

• Solve applications involving exponential modeling.

The argument involves some kind of fallacy. Identify the fallacy.

When confronted with questions from the press about alleged​ scandals, a congressman replies that the allegations against him should be ignored since his accuser is part of a vast​ right-wing conspiracy.

A.

Limited choice

B.

Appeal to popularity

C.

Circular reasoning

D.

Personal attack​ (ad hominem)

Draw a Venn diagram with two circles showing the given relationship between two sets.

dogs and pets

Let Aequalsdogs and Bequalspets. Choose the correct answer below.

Fill in the remaining entries in the​ two-way table shown to the right.

A survey of 120 patrons at a restaurant gave the preferences for entrees and drinks shown to the right.

Fill in the missing entries in the table.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain your reasoning.

Based on the testimonials of dozens of people who have lost weight following my​ diet, I will prove to you that my diet works for everyone.

Choose the correct answer below.

A.

The statement makes sense. The diet would not have worked for so many people if it​ didn’t work for everyone.

B.

The statement does not make sense. Some of the testamonials might not be in support of the diet.

C.

The statement does not make sense. Test cases never constitute a proof.

D.

The statement makes sense. Because the diet worked for that many​ people, it follows necessarily that the diet works for everyone.

Rephrase the​ argument, if​ necessary, so that the first premise has the form all S are P or no S are P. Then draw a Venn diagram to determine whether the argument is valid. If​ possible, discuss the truth of the premises and whether the argument is sound.

​Premise:

Fried foods increase cholesterol.

​Premise:

Beans do not increase cholesterol.

​Conclusion:

Beans are not fried foods.

Let X represent beans in the Venn diagram. Which Venn diagram below shows the correct placement of the variable​ X?

A.

A Venn diagram has a circle labeled fried foods inside a circle labeled increase cholesterol. An x is marked outside the two circles.

fried foods

increase

cholesterol

X

B.

A Venn diagram has a circle labeled fried foods inside a circle labeled increase cholesterol. An x is marked inside the circle labeled fried foods.

fried foods

increase

cholesterol

X

C.

A Venn diagram has a circle labeled fried foods inside a circle labeled increase cholesterol. An x is marked on the edge of the circle labeled fried foods.

fried foods

increase

cholesterol

X

D.

A Venn diagram has a circle labeled fried foods inside a circle labeled increase cholesterol. An x is marked inside the circle labeled increase cholesterol.

fried foods

increase

cholesterol

X

Is the argument valid or​ invalid?

Valid

Invalid

Is the argument​ sound?

No

Yes

Give an answer and explanation for the following question.

Jose had 10 bagels and ate all but 7 of them. How many bagels were​ left?

There were

7 bagels left because he ate

3 of them.

The following argument gives several reasons for a particular political position. Identify at least one unstated issue that may be the real issue of concern.

I oppose the​ President’s spending proposal. Taxpayer money should not be used for programs that many taxpayers do not support. Excessive spending also risks increasing budget deficits. Greater deficits increase the federal​ debt, which in turn increases our reliance on foreign investors.

Choose the correct answer below.

A.

The speaker may have an ideological opposition to paying taxes.

B.

The speaker may want the country to depend more on foreign investors.

C.

The speaker may be opposed to the government spending money.

D.

The​ President’s spending proposal is significantly under budget.

Consider the following example of a fallacy. Complete parts a and b below.

Fifty years of searching has not revealed life on other​ planets, so life in the universe must be confined to Earth.

1. Identify the premise and conclusion of the argument. Choose the correct answer below.

A.

​Premise: Life in the universe must be confined to Earth.​ Conclusion: Fifty years of searching has not revealed life on other planets.

B.

​Premise: Fifty years of searching has not revealed life on other planets.​ Conclusion: Life in the universe may not be confined to Earth.

C.

​Premise: Fifty years of searching has not revealed life on other planets.​ Conclusion: Life in the universe must be confined to Earth.

D.

​Premise: Life in the universe may not be confined to Earth.​ Conclusion: Fifty years of searching has not revealed life on other planets.

1. Briefly describe how the stated fallacy occurs in the argument.

A.

The conclusion is stated as if it were caused by the premise

B.

The premise directs attention away from the conclusion.

C.

The conclusion is stated as if it were the only possible conclusion.

D.

The premise is stated according to a lack of evidence of the opposite of the conclusion.

In the following​ argument, identify the​ premise(s) and​ conclusion, explain why the argument is​ deceptive, and identify the type of fallacy it represents.

My little boy loves dolls and my little girl loves​ trucks, so​ there’s no truth to the claim that boys are more interested in mechanical toys while girls prefer maternal toys.

Identify the​ premise(s) and conclusion of the argument. Choose the correct answer below.

A.

​Premise: My little boy loves dolls and my little girl loves trucks.​ Conclusion: It’s not true that little boys are more interested in mechanical toys and girls prefer maternal toys.

B.

​Premise: My little girl loves trucks.​ Conclusion: It’s not true that little boys are more interested in mechanical toys and girls prefer maternal toys.

C.

​Premise: My little boy loves dolls.​ Conclusion: It’s not true that little boys are more interested in mechanical toys and girls prefer maternal toys.

D.

​Premise: It’s not true that little boys are more interested in mechanical toys and girls prefer maternal toys.​ Conclusion: My little boy loves dolls and my little girl loves trucks.

Explain why the argument is deceptive. Choose the correct answer below.

A.

The conclusion is based on a personal allegation and stated as if it were caused by the premise.

B.

The premise is stated as the opposite as the conclusion and is drawn from an inadequate number of cases.

C.

The conclusion is drawn from an inadequate number of cases and uses ignorance about the truth to conclude the opposite.

D.

The conclusion is stated as if it were the only possible conclusion and uses ignorance about the truth to conclude the opposite.

Identify the type of fallacy the argument represents. Select all that apply.

A.

personal attack

B.

appeal to ignorance

C.

hasty generalization

D.

circular reasoning

E.

limited choice

For the categorical proposition given​ below, do the following.

1. If​ necessary, rephrase the statement in standard form.
2. State the subject and predicate sets.
3. Draw a Venn diagram for the proposition and label all regions of the diagram.
4. Based only on the Venn diagram​ (not on any other knowledge you​ have), answer the question that follows each proposition.

Students run. Is it true that no walkers are students​?

1. Does the categorical proposition need to be​ rephrased?

A.

Yes. The standard form is​ “Some students are people who do not run​.”

B.

Yes. The standard form is​ “Some students are people who run​.”

C.

Yes. The standard form is​ “No students are people who run​.”

D.

Yes. The standard form is​ “All students are people who run​.”

E.

No. The proposition is in standard form.

1. Which set is the subject set​ S?

A.

students that run

B.

people who run

C.

people who do not run

D.

students

Which set is the predicate set​ P?

A.

people who run

B.

people who do not run

C.

students

D.

students that run

1. If S is the subject set and P is the predicate​ set, which of the diagrams below is the correct Venn​ diagram?

A.

S

P

A Venn diagram contains two intersecting circles labeled S and P.

B.

S

P

A Venn diagram contains two non-intersecting circles labeled S and P.

C.

S

P

A Venn diagram contains two circles labeled P and S. Circle S is completely inside circle P.

1. Answer the question based only on the Venn diagrams. Is it true that no walkers are students​?

Yes. Because S and P do not​ overlap, if a member is not in​ P, then it must be in S.

B.

No. Because S and P do not​ overlap, the statement need not be true.

C.

No. Because P contains all of S. If something is in​ P, then it must also be in S.

D.

Yes. Because  P and S​ overlap, things not in P must be in S.

E.

No. Because P and S​ overlap, things not in P do not need to be in S.

F.

Yes. Because P contains all of S. If something is not in​ P, then it cannot be in S.