Review Standard Form exercises

Translation exercises

Here are some review statements regarding syllogisms. Practice putting them into Standard Form.  The answers are provided below.  Conversion, obversion, and contraposition are discussed in 7.2.

1. If a term is distributed in the conclusion, it needs to be distributed in the premise.

2. Syllogisms with two negative premises are invalid.

3. Syllogisms with a negative conclusion aren’t valid unless they have a negative premise.

4. An undistributed middle term is enough to make a syllogism invalid.

5. An argument with universal premises can’t have a particular conclusion.

6. Universal affirmatives and particular negatives have opposite truth values.

7. Necessary conditions go in the consequent.

8. Venn diagrams exhibit validity and invalidity.

9. You can construct a counterexample for any invalid argument.

10. Validity is a necessary condition for soundness.

 

Answers.

 

1. If a term is distributed in the conclusion, it needs to be distributed in the premise.

All terms that are distributed in a conclusion are terms that have to be distributed in a premise.

No terms that are distributed in a conclusion are terms that can be undistributed in a premise. (obverse)

 

2. Syllogisms with two negative premises are invalid.

No syllogisms with two negative premises are valid arguments.

No valid syllogisms are syllogisms with two negative premises. (converse)

All valid syllogisms are syllogisms that do not have two negative premises. (obverse)

 

3. Syllogisms with a negative conclusion aren’t valid unless they have a negative premise.

All valid syllogisms that have a negative conclusion are syllogisms that have a negative premise.

No valid syllogisms that have a negative conclusion are syllogisms with two affirmative premises. (obverse)

4. An undistributed middle term is enough to make a syllogism invalid.

All syllogisms with an undistributed middle term are invalid syllogisms.

No syllogisms with an undistributed middle terms are valid syllogisms. (obverse)

No valid syllogisms are syllogisms with an undistributed middle term. (converse)

All valid syllogisms are syllogisms with a distributed middle term. (obverse)

(The shorthand for the obverse of the converse of the obverse is the “contrapositive.”)

 

5. An argument with universal premises can’t have a particular conclusion.

No valid argument with universal premises is an argument with a particular conclusion.

 

6. Universal affirmatives and particular negatives have opposite truth values.

All A statements are statements that have opposite truth values to O statements.

No A statement is a statement that has the same truth value as an O statement. (obverse)

 

7. Necessary conditions go in the consequent.

All conditions that are necessary conditions are conditions that go in the consequent.

No necessary conditions are conditions that go in the antecedent. (obverse)

 

8. Venn diagrams exhibit validity and invalidity.

All Venn diagrams are diagrams that exhibit validity or invalidity.

 

9. You can construct a counterexample for any invalid argument.

All invalid arguments are arguments for which counterexamples can be constructed.

All people identical to you are people who can construct counterexamples for invalid arguments. ?

 

10. Validity is a necessary condition for soundness.

No sound arguments are invalid arguments.

All sound arguments are valid arguments. (obverse)

All invalid arguments are unsound arguments. (contrapositive)

 

 

2 Responses to Review Standard Form exercises

  1. Pingback: ingenieurs marocains

  2. Pingback: traiteur rabat

Leave a Reply

Your email address will not be published. Required fields are marked *