# IQ Test Labs

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### Valid arguments in syllogism

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:

### Valid forms of syllogistic arguments

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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'.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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.

#### Example::

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'.

#### Example::

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.