**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)

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