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There are 256 logically distinct types of syllogism, and only twenty four valid types. Here is the complete list of the types, labeled with mnemonic names and grouped by similarity:

Premises:

Some A is B

Some C is A

Conclusion:

All C is A

Similar to case 2. The middle terms are switched with the predicate and subject.

Rule 1: When statements are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 5: C is distributed in both the conclusion and the minor premise.

Premises:

All B is A

All C is B

Conclusion:

Some C is A

Similar to case 2. The middle terms are switched with the predicate and subject.

Rule 1: When statements are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Premises:

No B is A

All C is B

Conclusion:

No C is A

Similar to case 10.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

No B is A

All C is B

Conclusion:

Some C is not A

Similar to case 10.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All B is A

Some C is B

Conclusion:

Some C is A

Rule 1: When the premises are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Premises:

No B is A

Some C is B

Conclusion:

Some C is not A

Rule 2: When 'No' appears in a statement, 'Some-not' should follow as a valid possible conclusion.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All A is B

No C is B

Conclusion:

No C is A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All A is B

No C is B

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Baroco

Premises:

All A is B

No C is B

Conclusion:

No C is A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

Some B are not A

All B are C

Conclusion:

Some C are not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All A is B

All B is C

Conclusion:

Some C is A

Rule 1: When both premises are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Premises:

No B is A

All B is C

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All B is A

All B is C

Conclusion:

Some C is A

Rule 1: When the premises are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Premises:

No A is B

All C is B

Conclusion:

No C is A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

No A is B

All C is B

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

No A is B

Some C is B

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All B is A

Some B is C

Conclusion:

Some C is A

Rule 1: When the premises are positive, then the conclusion must be positive.

Rule 3: The middle term, B, is distributed in the major premise.

Rule 10: If a statement begins with 'some', the conclusion must begin with 'some'.

Premises:

Some B is C

No C is B

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All A is B

No B is C

Conclusion:

No C is A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 5: C is distributed in the conclusion and the minor premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

All A is B

No B is C

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

No A is B

All B is C

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.

Premises:

Some A is B

All B is C

Conclusion:

Some C is A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 9: If a statement begins with 'some', the conclusion must begin with 'some'.

Premises:

No A is B

Some B is C

Conclusion:

Some C is not A

Rule 3: The middle term, B, is distributed in the major premise.

Rule 4: A is distributed in the conclusion and the major premise.

Rule 7: If one statement is negative, the conclusion must be negative.