# Deductive Reasoning (Syllogisms) Explanation

Deductive Reasoning is a part of the assessment that many people have a hard time with. This is actually unnecessary because in fact there are only a few different types of questions. It is important to work very precisely and draw a Venn diagram to make the exercise clear to yourself. At the beginning you will probably make a lot of mistakes, but if you practice a lot and do the same thing every time, you will work faster and make fewer and fewer mistakes.

Exercises are mostly in the form:

Premise 1: there is a relationship between A and B

Premise 2: there is a relationship between A and C (or B and C)

Question: What conclusion can be drawn from this?

For A, B and C, often words are used that can confuse you. It is therefore important not to look at the meaning of the words in the propositions, but simply to show in a figure exactly what the proposition indicate about the relationships between A, B and C.

An example of a question that can confuse you is:

What logical conclusion can be drawn from the following two statements?

1: All the people who are easily angered are evil people

2: All the people who are easily angered are people who are angry

Conclusion:

• There are evil people who are not people who are easily angered
• people who are angry are always evil people
• there are evil people who are not people who are angry
• no one who is evil is someone who is angry
• There are evil people who are angry people

You should not think about what these statements mean, because very often they mean nothing at all. Just write down precisely what is A, B and C.

A: People who are easily angered

B: Evil people

C: People who are angry

Translated:
1: All A are B

2: All A are C

We make a figure of the propositions:

Now you have to see which of the positions is a green or red area, because a conclusion must always be made with certainty.

• There are evil people who are not people who are easily angered

Translated: Some B are not A

You see that it cannot be said with certainty that part of B is not A. It is only certain that part of B is A.

• People who are angry are always evil people

Translated: All C are B

This statement should be represented by a green area. But you can see that some parts of C are orange, so this statement cannot be made with certainty.

• There are evil people who are not people who are angry

Translated: Some B are not C

You see that it cannot be said with certainty that there is a part of B that is not C. Only that part of B is C (namely in area A).

• No one who is evil is someone who is angry

Translated: No B is C

This statement cannot be true, because area A is in both B and C. So there is a part of the collection B that falls within the collection C.

• There are evil people who are angry people.

Translated: Some B are C

This statement is correct. The green area is within both B and C, so there must be B that is C.