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What is Deductive Logic?
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypotheses. A deductive argument is valid if the conclusion does follow necessarily from the premises, i.e., if the conclusion must be true provided that the premises are true. A deductive argument is sound if it is valid and its premises are true. Deductive arguments are valid or invalid, sound or unsound, but are never false nor true. Deductive reasoning is a method of gaining knowledge. An example of a deductive argument:
1. All men are mortal
2. Socrates is a man
3. Therefore, Socrates is mortal
– Wikipedia

In actuality, Deductive Logic is a subject in the vast field of Philosophy that finds itself in MBA entrance examinations.

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Terms for Deductive Logic

A deductive logic question can be broken down into two parts:
1. Facts or Premise
2. Conclusion or Result
Facts or Premise form part of the information provided to us and the conclusion is the result we arrive at. For example, have a look at the following:
All actors are celebrities. =Fact/Premise
Bahrukh is an actor. =Fact/Premise
Bahrukh is a celebrity. =Conclusion/Result.

Conditions for Deductive Logic

The following are the conditions that you need to keep in mind while solving Deductive Logic Questions:
Facts/premises are always assumed to be correct. For example, if the author says apples are black in color, we assume it to be correct.
The conclusion to be valid has to be true as well as consistent. Consistent here means always true. For example, have a look at the following example:
1. Some men are great.
2. Some great are stupid.
3. Some men are stupid.
In the given case, the conclusion above is true but not always true, that is it is not consistent. Can you figure out the reason why it is not consistent?
The above covers the basic introduction for the topic. Let us now shift to the first part of the topic, syllogisms.

Syllogisms

Syllogisms are nothing else but a group of statements where one needs to establish a logical relationship between the facts and the conclusion. Remember that the conclusion that one derives in syllogism has to be valid in nature. We define a valid conclusion as one that is true as well as consistent. It is an absolute must that we keep these conditions in mind when answer the questions.
For example, have a look the two examples (the 3rd statement in the set is the conclusion)
Case 1:

  1. All human beings breathe.
  2. All those who breathe consume food.
  3. All human beings consume food.

The conclusion above is true as well as consistent: hence, valid.
Case 2:

  1. All human beings breathe.
  2. All those who breathe consume food.
  3. All those consume food are human beings.

Observe the clever play of words in the two cases. The second case incorrectly labels all those who consume food as human beings. This is not the case we do not know one condition: things that breathe who consume food and are not human beings. There is a possibility for such things to exist. Hence, we cannot assume automatically that all who consume food are human beings.
If you have a look at the above statements, you would realize that the conclusion as well as the premise is structured in the same way. This enables us to study the various possible cases of premise possible. The following are four case forms:
1. All A are B
This premise is used in the following ways:

  1. All men are mangoes.
  2. All idiots are intelligent.
  3. All gold glitters.

But what does this premise means? The meaning of each individual statement is explained below:

  1. All men are mangoes: each and every man is mango, but there can be a greater number of mangoes.
  2. All idiots are intelligent: all idiots are intelligent, and there can be some intelligent that are not idiots.
  3. All gold glitters: Gold will glitter for sure but the reverse might not be true. There might be a few things that glitter and are not gold.

So basically, All A are B means that each and every A has to be B. The reverse may or may not be true.
The above premise can be student through Venn diagrams as well. Have a look at the presentation to see the representation.

  1. No A is B
    When we say No A is B, it means no A is B.
    When we say ‘No man is a women’, it is understood, isn’t it
    When we say ‘No apple is a mango’, it is again understood.
    And if we are given, ‘No men are idiots’, we again take it to be valid. Remember, the premise is always correct. So if this statement is provided to us as a premise, we assume it to be correct. Just remember the meaning of the statement.
    The above premise can be student through Venn diagrams as well. Have a look at the presentation to see the representation.
    3. Some A are B
    When we say ‘Some men are crazy’, what precisely do we mean:
  1. Are almost all men crazy?
  2. Are just a few men crazy?
  3. At maximum, all minus one man are crazy?
  4. Or at least one man is crazy?

In conventional language, the use of some would imply that some men are crazy and some are not. But in deductive logic, this is not the case. We focus only on the information provided to us: that information labels some as crazy. For this to be valid, at least one will have to be crazy. How many are actually crazy is something that we do not know. This means that only one can be crazy, 10 per cent can be crazy or in fact, all can crazy. None of these cases is denied, and hence is valid.
The basic crux of the matter is: some men are crazy means that at least one man is crazy. Some A are B means that at least one A is B. That is all that you need to keep in mind for this premise.
In order to develop a deeper understanding, have a look at the Venn diagrams provided in the presentation.
4. Some A are B
Let us use some plain and simple logic here:
If some A are B= at least one A is B, then
Some A are not B= at least one A is not B.
The reasoning for such a result is the one for some A are B. When we say some men are not crazy, all we know is that there has to be one man that is not crazy. How such are there? We do not know. How many such can be there at max.? The maximum number is the complete set of men, all are not crazy. Keep in mind that this gives us the same result as No men are crazy.
In order to develop a deeper understanding, have a look at the Venn diagrams provided in the presentation. 
This completes the 4 case forms of premise. The learning from above can be applied to the assignment provided for this topic.

Logical Consistency

The first part of our study concerned deductive reasoning in the form of syllogisms. The second part concerns logical consistency. What is logical consistency?
Take a look at the following example: I will be born only if my mother pregnant.There are four possible cases that emerge out of this condition:

  1. My mother is pregnant.
  2. I am born.
  3. My mother is not pregnant.
  4. I am not born.

If we consider case 1, my mother is pregnant, what happens to me? I am born or not?
If you think about it, the parent condition only tells us that when I am born, my mother will be pregnant. The other way around is something I am not sure of. My siblings could also be born. This is what logical consistency is all about: taking case of these statements and their various fallouts.  An analysis of the above four conditions would look something like this:

  1. My mother is pregnant= I may or may not be born.
  2. 2. I am born= My mother is pregnant.
  3. 3. My mother is not pregnant= I am not born.
  4. I am not born= My mother may or may not be pregnant.

The above is one form of conditional statements that we are going to study. There are three more conditional statements that we are going to study. These are going to be on the basis of the conditional word that we use, that is if, only if or either-or.
Conditional One: IF, when, whenever
The statements based on the word if are ones where the cause acts as a sufficient condition for the effect. But wait a minute. What is the cause and what is the effect? And what is sufficient blah blah blah?
Just have a look at the following: We get fat if we eat junk food. (simple enough statement)
In this statement, the cause is: ‘we eat junk food’.
And the effect is: ‘we get fat’.
Pretty simple to arrive at the cause and effect? Always remember that the use of conditional words such as if, when, only if etc. will create such cause and effect relationships in the statement.
Back to our parent condition: we get fat if we eat junk food.
We have the following four cases:

  1. We eat junk food.
  2. We get fat.
  3. We do not eat junk food.
  4. We do not get fat.

And if carry out the same analysis as we carried out for only if, we get the following results:

  1. We eat junk food= we get fat for sure.
  2. We get fat= we may have eaten junk food or there might be some other cause for us getting fat.
  3. We do not eat junk food= we might get or we might not, there might be other reasons for us getting fat.
  4. We do not get fat= we have not eaten junk food for sure else we would have gotten fat.

This is the sample analysis of the ‘if-then’ condition.
As a further aid, you can use the following set of rules to help you out:
‘If A, then B’ means:

  1. A implies B
  2. B may or may not imply A
  3. Not A may or may not imply not B
  4. Not B implies Not A for sure

Another point: we said above that ‘if-then’ is a sufficient condition for the effect to occur, all that means is that in such a case, the effect is a necessary outcome of the cause but is not limited to the single cause, there can be other causes for it to occur.
In order to develop a deeper understanding, have a look at the examples provided in the presentation.
Conditional Two: Only if, only  when
We have already what the ‘only if’ looks like when we studied the example given above in the introduction to logical consistency.
As a further aid, you can use the following set of rules to help you out:
‘Only If A, then B’ means:

  1. A does not imply B
  2. B implies A
  3. Not A implies not B
  4. Not B may or may not imply not A.

Also, remember that only if is a necessary condition, that is if the effect occurs , it will only do so if the cause takes place: the cause is necessary for the effect to take place.
In order to develop a deeper understanding, have a look at the examples provided in the presentation.
Conditional Three: If & Only if, If & only when
This is the simplest one: just an addition of the above two.
As a further aid, you can use the following set of rules to help you out:
‘If and only if A, then B’ means:

  1. A implies B
  2. B implies A
  3. Not A implies not B
  4. Not B implies not A.

In order to develop a deeper understanding, have a look at the examples provided in the presentation.
Conditional Four: Either A or B
The conventional meaning for either A or B is if one happens, then the other does not (and vice versa). But this is where logic tricks us. Logic simply labels the ‘either-or’ condition as one where if one happens, there may be the possibility of the other happening. Whereas, if we label that one condition is not taking place, this would mean definite affirmation for the other (and hence it takes place)
In a set of simple rules, all it means is this:
‘Either A or B’ means:

  1. Not A implies B
  2. Not B implies A
  3. A may or may not imply not B
  4. B may or may not imply not A

In order to develop a deeper understanding, have a look at the examples provided in the presentation.