Chapter 9: CATEGORICAL SYLLOGISMS
- Practice on Rules -

Multiple Choice:
Click on the button next to the answer you wish to select. Your results will be displayed immediately in the question's text box.

No. of Questions= 21

In this exercise, you will be given a categorical syllogism, and asked to determine whether it is valid or invalid using the rules of validity.

To determine validity, you must use the method of rules.

Rules of Validity

In order to be valid, a categorical syllogism must satisfy all four of the following rules; if it violates one or more, it is invalid.

1) The middle term must be distributed in at least one premise.
2) If a term is distributed in the conclusion, it must be distributed in the premise in which it occurs.
3) The premises cannot both be negative.
4) If one premise is negative, the conclusion must be negative; if the conclusion is negative, one premise must be negative.


1 All M is P
No S are M
Therefore, No S is P

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
2 Some M are not P
All M are S
Therefore, some S are not P

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
3 All P are M
All M are S
All S are P

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
4 All Q is N
Some M is Q
Therefore, some M is N

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
5 No A are D
Some A are B
Therefore, some B are not D

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
6 All B are D
No C are B
Therefore, No C are D

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
7 All M are N
Some P are not M
Therefore, some P are not N

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
8 No B are D
All A are D
Therefore, no A are B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
9 All W are Y
No X are W
Therefore, some X are not Y

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
10 All D are B
Some D are A
Therefore, some A are B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
11 All B are A
Some C are not A
Therefore, some C are not B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
12 All N are P
Some P are M
Therefore, some M are N

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
13 All N are P
Some P are M
Therefore, some M are N

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
14 No A are B
Some C are A
Therefore, some C are B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
15 Some D are A
All C are A
Therefore, some C are D

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
16 No B are D
Some D are A
Therefore, some A are not B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
17 Some Q are M
No M are P
Therefore, some P is not Q

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
18 No B are D
Some A are D
Therefore, some A are B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
19 All W are Y
Some W are X
Therefore, all X are Y

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
20 All D are C
Some D are B
Therefore, some B are C

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.
21 Some A are not B
No A is C
Therefore, some C are not B

This syllogism is:

a) Valid.
b) Invalid: the middle term is not distributed in at least one premise.
c) Invalid: a term is distributed in the conclusion, but is not distributed in the premise in which it occurs.
d) Invalid: the premises are both negative.
e) Invalid: one premise is negative, but the conclusion isn't negative, or the conclusion is negative, but one premise isn't negative.


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