VENN DIAGRAM REASONING TRICKS

Syllogism is a ‘Greek’ word that means inference or deduction. As such inferences are based on logic, then these inferences are called logical deduction. These deductions are based on propositions (premise).

Different types of questions covered in this section are as follows :

• Two Statements and Two Conclusions

‘Syllogism’ checks basic aptitude and ability of a student to derive inferences from given statements using Venn diagrams and reasoning r solving problems.

Four types of statements :

(i) All A is B

(ii) Some A is B

(iii) Some A is not B

(iv) No A is B

All A is B

Conclusions :

True Some A is B Some B is A

False No A is B No B is A

Some A is B

Conclusions :

True Some B is A

False No A is B No B is A

Some A is not B

Conclusions :

True Nil

False Some B is not A

No A is B

Conclusions :

True No B is A Some A is not B Some B is not A

False Some A is B Some B is A All A is B All B is A

Directions : Each of the following questions contains two statements followed by two conclusions numbered I and II. You have to consider the two statements to be true, even if they seen to be at variance at the commonly known facts. You have to decide which of the given conclusions definitely follows from the given statements.

Give answer (a) if only I follows; (b) if only II follows; (c) if either I or II follows; (d) if neither I nor II follows and (e) if both I and II follow.

Question 1 :

Statements :

Some chairs are glasses

All trees are chairs

Conclusions :

I. Some trees are glasses

II. Some glasses are trees

Answer :

Some chairs are glasses :

All trees are chairs :

From the above diagrams, the answer is

(d) neither I nor II follows

Question 2 :

Statements :

No man is a lion

Ram is a man

Conclusions :

I. Ram is not a lion

II. All men are not Ram

Answer :

No man is a lion :

Ram is a man :

From the above diagrams, the answer is

(a) only I follows

Question 3 :

Statements :

All boys are Fathers

All Fathers are Mothers

Conclusions :

I. All Fathers are boys

II. All boys are Mothers

Answer :

All boys are Fathers :

All Fathers are Mothers :

From the above diagrams, the answer is

(b) only II follows

Question 4 :

Statements :

All pens are cups

All cups are bowls

Conclusions :

I. All pens are bowls

II. All cups are pots

Answer :

All pens are cups :

All cups are bowls :

From the above diagram, it is clear that "All pens are bowls". So the first conclusion is true.

In the second conclusion we find the object "Pots". But, the object "Pots" is not a part of either of the two given statements. So, we don't have enough information to decide about the second conclusion. 

Therefore, the answer is

(a) only I follows

Question 5 :

Statements :

All students are boys

No boy is dull

Conclusions :

I. There are no girls in the class

II. No student is dull

Answer :

All students are boys :

No boy is dull :

or

From the above two diagrams, it is clear that "No boy is dull". So, the first conclusion is true.

From the first statement "All students are boys", it is clear that "There are no girls in the class". So, the second conclusion is also true.

Therefore, the answer is

(e) both I and II follow

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