Logical Reasoning - Syllogism

Logical Reasoning skills

Logical Reasoning - Syllogism 

1. Direction (1-7) : In each of the questions below three statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts.

1. Statements: Some buildings are white.

All whites are oranges.

Some oranges are boxes.

Conclusions: I. Some boxes are buildings.

II. Some oranges are buildings.

Answer: If only conclusion II follows.

Explanation:

Some buildings are white + All whites are oranges = I + A = I

Some buildings are oranges - conversion - some oranges are buildings (I).

Hence II follows.

Some buildings are oranges + Some oranges are boxes = I + I = No Conclusions.

Hence I does not follow..

2. Statements: All desks are mirrors.

All mirrors are chairs.

Some chairs are pens.

Conclusions: I. Some pens are desks.

II. Some chairs are desks.

Answer: If only conclusion II follows.

Explanation:

All desks are mirrors + All mirrors are chairs = A + A = A

= All desks are chairs - conversion - some chairs are desks (I).

Hence II follows.

All desks are chairs + some chairs are pens = A + I = No conclusions.

Hence I does not follows.

3. Statements: All dollars are rupees.

No rupee is yen.

No rupee is pound.

Conclusions:

I. Some pounds are not dollars

II. Some dollars are not yens

Answer: Both I and II follow

Explanation:

I. All dollars are rupees + No rupees is pound = All + No = No

= No dollars is pound

=> Some pounds are not dollar.

Hence I is true

II. All dollars are rupees.

No rupee is yen= All+ No = No

= No dollars is yen

=> Some dollars are not yen is true.

4. Statements: Some glasses are rivers.

Some rivers are bottles.

Some bottles are plates.

Conclusions: I. Some plates are rivers.

II. Some bottles are glasses.

Answer: If neither conclusion I nor conclusion II follows.

Explanation:

I + I = No conclusions.

5. Statements:

No books is a pen.

All pens are pencils.

All pencils are erasers.

Conclusions:

I. All pens are erasers.

II. At least some erasers are pencils.

Answer: If both conclusions I and II follows.

Explanation:

All pens are pencils

All pencils are erasers.

A + A = A - type of Conclusion

"All pens are erasers."

This is conclusion I.

Conclusion II is Converse of the second Premise.