Conversion, Contraposition, Obversion Exercises

Instructions: Translate each claim below into a standard-form categorical claim. Then, do 2 immediate inferences on it (either a conversion or a contraposition AND an obversion). Then, match the numbered claims with the lettered claims that are equivalent. (i.e., 9 is equivalent to g, 14 is equivalent to s, etc.). In order to do this, you will have to translate the lettered claims into standard form, as well, and possibly do several immediate inferences on each of them. SHOW ALL YOUR WORK!! Note: Some letters can be used for more than one number.

1. Some people who have not been tested can give blood.

2. People who have not been tested cannot give blood.

3. Nobody who has been tested can give blood.

4. Nobody can give blood except those who have been tested.

a. Some people who have been tested cannot give blood.

b. Not everybody who can give blood has been tested.

c. Only people who have been tested can give blood.

d. Some people who cannot give blood are people who have been tested.

e. If a person has been tested, then she cannot give blood.

Immediate Inferences Exercises

Answers:

1. Some people who have not been tested can give blood.

Some [people who have not been tested] are [people who can give blood] (I-claim)

Converse: Some [people who can give blood] are [people who have not been tested]

Obverse: Some [people who have not been tested] are not [people who cannot give blood]

ANSWER 1=b (see below)

2. People who have not been tested cannot give blood.

All [people who have not been tested] are [people who cannot give blood] (A-claim)

Contrapositive: All [people who can give blood] are [people who have been tested]

Obverse: No [people who have not been tested] are [people who can give blood]

ANSWER 2 = c (see below)

3. Nobody who has been tested can give blood.

No [people who have been tested] are [people who can give blood]  (E-claim)

Converse: No [people who can give blood] are  [people who have been tested]

Obverse: All [people who have been tested] are [people who cannot give blood]

ANSWER 3 = e (see below)

4. Nobody can give blood except those who have been tested. = The only people who can give blood are those who have been tested.   OR   Only those who have been tested can give blood.

All [people who can give blood] are [people who have been tested]

Contrapositive: All [people who have not been tested] are [people who cannot give blood]

Obverse: No [people who can give blood] are [people who have not been tested]

ANSWER: 4 = c


Lettered claims:

a. Some people who have been tested cannot give blood.

Some [people who have been tested] are [people who cannot give blood] (I-claim)

Converse: Some [people who cannot give blood] are [people who have been tested]

Obverse: Some [people who have been tested] are not [people who can give blood]

b. Not everybody who can give blood has been tested.

Some [people who can give blood] are not [people who have been tested] (O-claim)

Contrapositive: Some [people who have not been tested] are not [people who cannot give blood] 

Obverse: Some [people who can give blood] are [people who have not been tested]

So, 1 = b

c. Only people who have been tested can give blood.

All [people who can give blood] are [people who have been tested] (A-claim)

So, 2 = c and 4 = c

d. Some people who cannot give blood are people who have been tested.
 
Some [people who cannot give blood] are [people who have been tested] (I-claim)

e. If a person has been tested, then she cannot give blood.

All [people who have been tested] are [people who cannot give blood] (A-claim)

So, 3 = e