Reasoning Syllogism-1

Inference drawn from argument

We can see a lot of argumentative questions in reasoning tests like argument-inference, statement- conclusion, statement- argument or statement- assumption. Let us examine questions related to inferences drawn from argument. In these modes of questions, a statement or statements are given and two or more inferences follow. By using the rules of formal logic you have to find out which of the statements can be inferred from the given statement
Example: Most men who stop drinking gain health
Inferences:
If you stop drinking you can gain health
If you do not stop drinking you can not gain health
Here both inferences are not correct because most men is not a general statement.

Now try to answer the following questions. There are two statements followed by two inferences. Decide which inference can be drawn from the statements.
Choose from the following answer choices:
1. only conclusion 1 is true
2. only conclusion2 is true
3. either 1 or 2 is true
4. neither 1 nor 2 is true
Q. 1 Statement: 1. Professor who teach PG do not engage Degree classes
  Statement: 2. Chandrasekhar is a professor
Inference:
1. Chandrasekhar teaches PG
2. Chandrasekhar teaches Degree

Q. 2 Statement: 1. Sreeja is studying for LLB
  Statement: 2. Sreeja can remember things well
Inference:
1. Sreeja can pass LLB
2. Remembering things well is a need for passing

Q. 3 Statement: 1. Majority of the students are idiots
Statement: 2. Majority of the students are girls
Inference:
1. Minority of the students are intelligent
2. Minority of the students are boys.

In statement conclusion type a conclusion has to be drawn from the statement.

Examples:
Mary is a girl
All girls are beautiful
So Mary is beautiful
Here the propositions 1 and 2 are statements or premises and the proposition three is the conclusion derived from the two statements.
In this syllogism the subject of the conclusion is known as Minor term and predicate of the conclusion is known as Major term. Middle term is common to both the statements. In the above example beautiful is the predicate (Major Term) Mary is the subject (Minor term) and girl is the middle term. It does not occur in the conclusion.
Some examples:

Statement: 1. some cats are dogs
Statement: 2. all dogs are rats
Inference:
3. all rats are dogs
4. some cats are rats.
Here inference 1 can not follow because no term can be distributed in the conclusion unless it is distributed in the statements.
Another type:
Statement: 1. all cats are dogs
Statement: 2. some dogs are wild
Inference:
1. all dogs are cats
2. some cats are wild.
Here no conclusion follows the statement because the middle term dog is not distributed at least once in the premises.
If one statement is negative, the conclusion must be negative.
Statement: 1. All dogs are cats
Statement: 2. No cat is rat
Inference:
1. Some rats are dogs
2. No dog is rat
Here the first conclusion is wrong.
If one statement is particular the conclusion must be particular
Statement: 1. some dogs are cats
Statement: 2. all cats are rats
Inference:
1. Some dogs are rats
2. All rats are cats
Here the conclusion 2 is not following because one premise is particular.

If both statements are affirmative in nature the conclusion would be affirmative. If the major premise is affirmative the conclusion must be particular .
Statement: 1. all dogs are cats
Statement: 2. all cats are rats
Inference:
1. all dogs are rats
2. some dogs are not rats
Statement: 1. all dogs are cats
Statement: 2. some rats are dogs
Inference:
1. some rats are cats
2. all cats are rats
Here the statement 2 is not following.
Exercise
Here two statements are given followed by two conclusions. Determine which conclusion is following the statements. Give answer A if only Conclusion 1 follows, B if only Conclusion 2 follows, C if either 1 or 2 follows and D if neither 1 nor 2 follows.
Q. 1 Statement:
All flowers are stems
All stems are root
Conclusion:
All roots are flowers
All stems are flowers
Q. 2 Statement:
All men are married
Some men are educated
Conclusion:
Some married are educated
Some educated are married
Q. 3 Statement:
Kings married only beautiful girls
Sakunthala is beautiful
Conclusion:
Sakunthala was married by a king
Sakunthala was not married by a king