# This is a kind of reasoning which is essential for competitive exams

In competitive exams this of a from of reasoning in which a conclusion is drawn and this is from two given or else assumed propositions which is premises and a common one or else middle term is present in the two premises but not in the conclusion, which may be invalid for example all dogs are animals, all animals have four legs, therefore all dogs have four legs. A deductive reasoning as distinct from induction. This is called as syllogism questionsThe questions which are asked in this those questions consist of two or more statements and those statements are followed by two or more than two conclusions. You have to find out right conclusion the may or may not would be logically follow from the given statements. The mentioned statements should have to be taken as true even if they think to be at variance from which the commonly known facts.

For such questions, you can take the help of ‘Venn diagrams’. On the mentioned of the given statements, you should have to draw all the possible diagrams, and then you have to find out the solution from each of these diagrams separately. Finally, the answer common to the all the diagrams is taken.

Example 1:

Statements:

1. All dogs are asses.
2. All asses are bulls

Conclusions:

1. Some dogs are not bulls
2. Some bulls are dogs
3. All bulls are dogs
4. All dogs are bulls

Solution:

On the basis of both statements, the following one diagram is possible.

From the diagram it is clear that (2) and (4) conclusions logically follow.

Example 2:

Statements:

1. Some dogs are asses
2. Some asses are bulls

Conclusions:

1. Some asses are not dogs
2. Some dogs are bulls

Solution:

From the given statements the following diagrams are can be possible:

From the diagram neither (1) nor (2) conclusion follow.

Syllogism 1

Directions to solve:

In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be a variance from commonly known facts. The conclusions and then decide which of the given conclusions logically follows from the two statements, disregarding commonly known facts.

• (A) if only (1) conclusion follows
• (B) if sonly (2) conclusion follows
• (C) if either (1) or (2) follows
• (D) If neither (1) nor (2) follows and
• (E) If both (1) and (2) follow
1. Statements: Some actors are singer. All the singers are dancers.

Conclusions:

1. Some actors are dancers
2. No singer is actor
3. Only (1) conclusion follows
4. Only (2) conclusion follows
5. Either (1) or (2) follows
6. Neither (1) nor (2) follows
7. Both (1) and (2) follow

Explanation:

1. Statements: All the harmoniums are instruments. All the instruments are flutes.

Conclusions:

1. All the flutes are instruments.
2. All the harmoniums are flutes
3. Only (1) conclusion follows
4. Only (2) conclusion follows
5. Either (1) or (2) follows
6. Neither (1) nor (2) follows
7. Both (1) and (2) follow