PHL Chapter 9

All places where there are snakes are places where there are frogs.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

There are frogs wherever there are snakes.

All times Joan sings are times people make faces.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

People make faces every time Joan sings.

All members of the suborder Ophidia are snakes.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

The only members of the suborder Ophidia are snakes.

All politicians I know are senators.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

The only politicians I know are senators.

All people who arrived are cheerleaders.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

Nobody arrived except the cheerleaders.

Some Arabs are not non-Christians.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

Find the obverse of "Some Arabs are Christians."

Some non-Hindus are not non-Indians.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

Find the contrapositive of "Some Indians are not Hindus."

No, this claim is not logically equivalent to the original claim.

Translate each of the following into a standard-form claim (in the exact form of an A-, E-, I-, or O-claim).  Instead of writing in your own answer, choose the best answer from the options provided.

Is the converse of "All Protestants are Christians" equivalent to the original claim?

Valid

Is this argument logically valid? "None of the people who arrived late were people who got good seats, so none of the good seats were occupied by latecomers.

All students who didn't write good essays are students who weren't admitted to the program.

Find the contrapositive of "All students who were admitted to the program are students who wrote good essays."

A - Universal Affirmative Standard Form

All S are P.

E - Universal Negation Standard Form

No S are P

I - Particular Negation Standard Form

Some S are P

O - Negative Particular Standard Form

Some S are not P

Categorical Operation - Conversion

• A-Claim: All S are P → All P are S

• E-Claim: No S are P → No P are S

• I-Claim: Some S are P → Some P are S

• O-Claim: Some S are not P → Some P are not S

Categorical Operation - Obversion

• A-Claim: All S are P → No S are non-P

• E-Claim: No S are P → All S are non-P

• I-Claim: Some S are P → Some S are not non-P

• O-Claim: Some S are not P → Some S are non-P

Categorical Operation - Contraposition

• A-Claim: All S are P → All non-P are non-S

• E-Claim: No S are P → No non-P are non-S

• I-Claim: Some S are P → Some non-P are non-S

• O-Claim: Some S are not P → Some non-P are not non-S

Obversion

Maintains Logical Equivalency with:  E-Claims, I-Claims, A-Claims, O-Claims

Conversion

Maintains Logical Equivalency with:  E-Claims & I-Claims

Contraposition

Maintains Logical with Equivalency: A-Claims, O-Claims