From Fogelin, R. J./W. Sinnott-Armstrong (2001) Understanding Arguments, 6^th ed., Wadsworth.  

Exercise VIII, Ch 9, p. 285

Indicate whether the following sentences claim that the underlined words express a necessary condition or a sufficient condition of the italicised words.

EXAMPLE: If you work hard, you will succeed.

SOLUTION: Your working hard is sufficient for your success.

1.                    Litmus paper will turn red if it is put in acid.

2.                    Litmus paper will turn red only if it is put in acid.

3.                    Litmus paper will not turn red if it is not put in acid.

4.                    Litmus paper will turn red if it is put in acid.

5.                    Litmus paper will not turn red provided that it is not put in acid.

6.                    You have to pass the final exam in order to pass the course.

7.                    Passing the final exam is all you have to do to pass the course.

8.                    If you don’t pass the final exam, you can’t pass the course.

9.                    If you pass the final exam, you can’t fail to pass the course.

10.                 You can’t pass this course unless you pass the final exam.

Exercise X, pp. 288-9

For each of the following tables decide

(a)                which, if any, of the candidates – A, B, C, or D – is not eliminated by the Sufficient Condition test;

(b)                which, if any, of the candidates – A, B, C, or D – is not eliminated by the Necessary Condition test;

(c)                which, if any, of the candidates – A, B, C, or D – is not eliminated by either test.

1.            Case 1:                    A                      B                        C                        D                        G

                        Case 2:                 ~A                        B                      ~C                        D                     ~G

                        Case 3:                   A                      ~B                        C                      ~D                        G

2.            Case 1:                    A                        B                        C                      ~D                        G

                        Case 2:                 ~A                        B                        C                        D                        G

                        Case 3:                   A                      ~B                        C                      ~D                        G

3.            Case 1:                    A                        B                        C                        D                      ~G

                        Case 2:                 ~A                        B                        C                        D                        G

                        Case 3:                   A                      ~B                        C                      ~D                        G

Exercise XII, pp. 302-3

In each of the following examples a strong correlation, either negative or positive, holds between the two sets of phenomena, A and B. Try to decide whether A is the cause of B, B is the cause of A, both are caused by some third factor, C, or the correlation is simply accidental. Explain your choice.

1.                    At one time there was a strong negative correlation between the number of mules in a state (A) and the salaries paid to professors at the state university (B). In other words, the more mules, the lower the professorial status.

2.                    It has been claimed that there is a strong positive correlation between those students who take sex education courses (A) and those who contract venereal disease (B).

3.                    LOCKED DOORS NO BAR TO CRIME, STUDY SAYS

Washington (UPI) – Rural Americans with locked doors, watchdogs or guns may face as much risk of burglary as neighbours who leave doors unlocked, a federally financed study says.

The study, financed in part by a three-year $170,000 grant from the Law Enforcement Assistance Administration, was based on a survey of nearly 900 families in rural Ohio.

Sixty percent of the rural residents surveyed regularly locked doors (A), but were burglarized more often than residents who left doors unlocked (B).

4.                    There is a high positive correlation between the number of fire engines in a particular borough in New York City (A) and the number of fires that occur there (B).

5.                    For a particular United States president, there is a negative correlation between the number of hairs on his head (A) and the population of China (B).