Four Premise Arguments

A Syllogism is a form of reasoning in which the conclusion is drawn from the given statements. Four Premises Arguments means that there are 4 statements and 1 or more conclusion. These are same as the three Premises arguments. They are also represented in the form of Venn Diagrams. Below are a few examples of four 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 four premise arguments, we are given four sentences or statements. On these four sentences, a question is set up. Following the sentences, conclusions will be present. Your simple job is to study these four arguments and make a mental picture or a Venn diagram model of some situation. Then compare this mental picture or the Venn Diagram to the conclusions present in the question. You will have to select the right and the wrong conclusions from the options. Let us start by seeing the examples of the Definite conclusion type questions.

Definite conclusions are those conclusions which are definitely true from the given Premises. In other words, these conclusions have to or must follow from the logic defined in the premise arguments. For example:

Example 1: Direction: In the following space, four statements and four conclusions are present. Some or all of the conclusions follow directly from the statements given below. Pick out the conclusion or conclusions that are correct based on the premise set by the statements below:

Statements:

1. All A are B

2.  All B are C

3. All C is D

4. Some E is B

Conclusions:

i. All A are C

ii. All A are D

iii. Some E is C

iv. All E is C

Answer: Let us denote all the A’s, B’s, C’s, D’s and E’s with the help of ellipses and circles as below. Since all A’s are B’s, this means that the ellipse or the circle for A would be inside the ellipse or the circle of B. Similarly it follows for other cases. Now we have that some E are B. This means that only some portion of the set E will overlap with B and can thus be shown as below:

From the Venn Diagram, we can see that the conclusions i, ii and iii i.e. all A are C, all A are D, & some E are C will definitely follow. The conclusion iv does not follow because we do not know anything about the part of E which lies outside all the circles.

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,

Statements:

1. All A are B

2. All B are C

3. All C is D

4. Some E is B

Conclusions:

1. All E being B is a possibility.

2. All D being A is a possibility

Solution:

We can solve this question by using the Venn Diagram.

Here both the conclusions i and ii follow

Explanation:

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

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

Other Types of Questions

Statements:

1. Some A is not B

2. Some B are C

3. Some D is C

4.No D is A

Conclusions:

i.No A is B

ii. All C are B

iii. Some D is A

iv. Some C is B

Solution:

We can solve this question by the below Venn Diagram

Here all conclusions i,ii and iii do not follow. Only conclusion iv follows.

Explanation:

For conclusion i:It is given that No A is B whereas in the statement it is given that Some A are not B which means that there is some part of A which is not B but we don’t know anything about the other parts of A. So we cannot make a conclusion that No A is B.

For conclusion ii: It is given that all C is B but in Statement, it is given that Some C is B so we cannot make any definite conclusion on the whole part of C.

For conclusion iii: It is given that Some D are A but we don’t have any direct relation between D and A so we cannot make any definite conclusion about them.

Practice Questions

1.Statements:

i. All Cats are Rats

ii. All Rats are Dogs

iii. All Dogs are Monkeys

iv. Some Horses are Rats

Conclusions:

i. Some Horses are Dogs

ii. Some Dogs are Cats

Solutions: Both conclusions i. and ii. follow.

2.Statements:

i. Some Tables are not Chairs

ii. Some Chairs are Desks

iii. Some Pens are Desks

iv.No Pen is Table

Conclusions:

i. All Tables are not Chairs is a possibility.

ii. Some Desks are Tables.

Solution: Only Conclusion i. follows.