Syllogism

Three Premise Arguments

A syllogism is a form of reasoning in which the conclusion is drawn from the given statements. Three Premise Arguments means that there are 3 statements and 1 or more conclusions. These are same as the two premise arguments. They are also represented in the form of Venn Diagrams. Below are a few examples of three premise arguments of definite conclusions as well as of that of possibility type of conclusions that will help you to understand these type of problems.

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Definite Conclusions

In the three premise arguments, three statements are given. These three statements can be used to draw conclusions or define possibilities. Conclusions are drawn when the statements directly lead to one of the cconclusions. Below each set of statements, a set of conclusions will be given. your job is to identify the correct option.

Definite conclusions are those conclusions which are definitely true from the given Premises. In the arguments, the premise is very important. The conclusions or the inference are drawn from the premise and the reasoning is entirely based on the premise. We will see a few statements below that will help us understand what definite statements are.

Example 1:

Statements:

I. All A are B

II. All B are C

III. Some D is A

Conclusions:

These are three statements or three premises of our arguments. Indefinite conclusions, these three statements will lead us to a unique conclusion. The conclusions in the question will be given like we have below:

Conclusions:

I. All A is C. This is one of the conclusions.

II. All A are D

III. Some D is B

A) I, II and III are correct

B) Only I and II are correct

C) Only II and III are correct

D) Only I and III are correct

Answer: We can solve this question similarly as we used to solve the Questions of 2 Premises by using the Venn Diagrams. We can use the Venn Diagrams to easily solve this question. In fact, to solve the questions on arguments, we will have to use the Venn diagrams. Let us see below:

Premise

From the Venn Diagram, we can see that the conclusions I and III definitely follow. So the correct option is D) Only I and III are correct.

Explanation: The conclusion II does not follow because in the statement it is given that Some D is A and in the conclusion, it is given that All A is D. There is some part of A about which we do not have any information so any definite conclusion about it will not follow.

Possibilities

Possibilities are those conclusions which are not definitely true but they may or may not be true. We can take the same example here as we saw above.

Statements:

I. All A are B

II. All B are C

III. Some D are A

Conclusions:

I. All D are A is a possibility.

II. All C are A is a possibility.

A) Both I, II are correct

B) Only I is correct

C) Only II is correct

D) The data is not sufficient

Answer: We can solve this question by using the Venn Diagram.

Three Premise Arguments

Here both the conclusions follow.

Explanation: For Conclusion I: For D we know that some part of D is A, B, C but we don’t know anything about the shaded part so everything about this shaded part becomes a possibility.

For Conclusion II: For C we know that some part of C is A but we don’t know anything about the remaining part of C so all the possibilities for the remaining part of C become true.

Hence the correct option is A) Both I, II are correct.

Other Types of Questions

Statements:

I. Some A is not B

II. Some B are C

III. Some D is C

Conclusions:

I. All A is not B is a possibility

II. Some B are D

Answer: We can solve this question by the below Venn Diagram. The cross in the red designates the relation “are not”. We can say that since some A are B, not all A are B. The following Venn Diagram represents the statements present in the above question.

Three Premise Arguments

Hence only the conclusion I follow.

Explanation: For Conclusion I: It is given that All A is not B is a possibility but in Statement I, it is given that Some A are not B so we cannot make any definite conclusion. So it becomes a possibility and all the possibilities are true.

For Conclusion II: It does not follow because no direct relation between B and D is given. The only relation is between C and D and between B and C.

Practice Questions

Q 1. Statements:

I. All Teachers are Lawyers

II. All Lawyers are Doctors

III. All Doctors are Engineers

Conclusions:

I. Some Engineers are Lawyers

II. Some Doctors are Teachers

A) Both are the wrong                   B) Both are correct                C) They may be correct             D) Data Insufficient

Ans: B) Both are correct

Q 2. Statements:

I. Some Trains are not Cars

II. Some Cars are Bikes

III. Some Scooters are Bikes

Conclusions:

I. All Trains are not Cars a possibility.

II. Some Scooters are Cars.

A) Both are the wrong                   B) Both are correct                C) I is correct             D) II is correct

Ans: C) I is correct

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