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Multiple premises

When evaluating the validity of deductive reasoning arguments that have multiple premises, it helps to gain confidence working with Euler diagrams.

Practice drawing accurate diagrams that represent the relationships between the statement types and which help to solve syllogisms visually.

Use syllogistic rules wherever applicable in order to narrow down the choices in the conclusions/options.

Cases similar to categorical syllogism arguments are shown according to each conclusion.

Multiple premises examples

Example 1:

Multiple premises example 1

1. All Aeons are Bakus.

2. All Bakus are Centaurs.

3. All Centaurs ae Griffins.

4. Some Griffins are Quinotaurs.


A. Some Quinotaurs are Bakus. (Case 6)

B. Some Griffins are Aeons. (Case 2)

C. Some Centaurs are Aeons. (Case 2)

D. Some Quinotaurs are Aeons. (Case 6)

Applicable rules: Rule 1, Rule 6

Example 2:

Multiple premises example 2

1. Some Tarasques are Wyverns.

2. All Wyverns are Yalis.

3. All Yalis are Zeta Reticulans.

4. Some Zeta Reticulas are Yumboes.


A. Some Yumboes are Wyverns. (Case 6)

B. Some Zeta Retuculans are Tarasques. (Case 6)

C. Some Yalis are Tarasques. (Case 6)

D. Some Yumboes are Tarasques. (Case 6)

Applicable rules: Rule 1, Rule 6

Example 3:

Multiple premises example 3

1. All Bakja Rakhnas are Yalis.

2. No Yali is Zashiki Bokko.

3. Some Zashiki Bokkos are Aeons.

4. All Aeons are Centaurs.


A. Some Centaurs are Bakja Rakhnas. (Case 6)

B. Some Centaurs are Zashiki Bokkos. (Case 7)

C. No Centaur is Bakha Rakhna. (Case 6)

D. Some Zashiki Bokkos are Bakha Rakhnas. (Case 6)

'B', and either 'A' or 'C' are valid (according to the merging concept).

Example 4:

Multiple premises example 4

1. Some Aeons are Bakus.

2. Some Centaurs are Bakus.

3. All Bakus are Griffins.

4. All Griffins are Yalis.


A. Some Aeons are Yalis. (Case 5)

B. Some Centaurs are Griffins. (Case 5)

C. Some Aeons are Centaurs. (Case 6)

D. No Aeon is a Centaur. (Rule 1)

Applicable rules: Rule 1.

'A', 'B', and either 'C' or 'D' are valid (according to the merging concept).

Example 5:

Multiple premises example 5

1. Some Yumboes are Tarasques.

2. All Tarasques are Quinotaurs.

3. Some Quinotaurs are Centaurs.

4. No Griffin is a Centaur.


A. No Griffin is a Yumboe. (Case 12)

B. All Centaurs being Yumboes is a possibility. (None/all possibility case.)

C. Some Quinotaurs are Yumboes. (Case 2)

Example 6:

Multiple premises example 6

1. Some Bakus are Centaurs.

2. All Centaurs are Wyverns.

3. Some Wyverns are Yalis.

4. All Yalis are Zerzurans.


A. All Zerzurans are Bakus. (Case 2)

B. Some Yalis are Bakus. (Case 6)

C. Some Zerzurans being Wyverns is a possibility. (Some/some possibility case.)

D. No Wyvern is a Baku (Rule 1)

None of the conclusions follow.