Logical Reasoning Test

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Logical Reasoning Test - 27

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Question 1
5 / -1

Read the given statements and conclusions carefully. Consider the information given in the statements as true even if it seems to be at variance with commonly known facts and then decide which of the given conclusions logically follow from the statements?

Statements:

All rats are cats.

Some cats are dogs.

Conclusions:

I. Some rats are dogs.

II. No rat is dog.

III. Some cats are rats.

A
Only conclusion II follows.

B
Only conclusion ||| follows.

C
Only conclusion I follows.

D
Both conclusions I and III follow.

Solution

Statements:

All rats are cats.

Some cats are dogs.

The least possible Venn diagram is as follows:

Conclusions:

I. Some rats are dogs. - False (because there is no direct relation given between rats and dogs, so it can be possible but not definite)

II. No rat is dog. - False (because there is no direct relation given between rats and dogs, so it can be possible but not definite)

III. Some cats are rats. - True (because All rats are cats given. So, Some cats are rats too)

Hence, the correct answer is "Only conclusion III follows".
Question 2
5 / -1

Directions For Questions

Study the given diagram carefully and answer the question that follows.

The numbers in different sections indicate themnumber of persons who can drive different vehicles.

...view full instructions

What is the difference between the number of persons who can drive all the three vehicles and that of persons who can drive any two of these vehicles?

A
27

B
15

C
12

D
21

Solution

According to the given information:

The number of persons who can drive all the three vehicles = 6

Persons who can drive any two of these vehicles = 8 + 7 + 12 = 27

Thus, the difference between the number of persons who can drive all the three vehicles and that of persons who can drive any two of these vehicles = 27 - 6 = 21

Hence, the correct answer is "21".
Question 3
5 / -1

Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.

Statements:

I. Some P are Q.

II. No Q is R.

Conclusions:

I. No P is R.

II. Some P are not R.

III. Some Q are P.

A
All conclusions follows

B
Only conclusion I follows

C
Both conclusions II and III follows

D
Both conclusions I and III follows

Solution

Given Statements:

I. Some P are Q.

II. No Q is R.

The possible Venn diagram is as follows,

Conclusions:

I. No P is R. - False (because there is no direct relation between P and R so it can be possible but not definite)

II. Some P are not R. - True (because, Some P are Q and No Q is R. So Some P are not R it is definite)

III. Some Q are P. - True (because, Some P are Q given. So Some Q are P it is definite)

Hence, the correct answer is "Both conclusions II and III follows".
Question 4
5 / -1

Which of the following is an example of a Categorical Syllogism?

A
If it rains, then the ground will be wet. It rained, so the ground is wet.

B
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

C
If I study, then I will pass the test. I studied. Therefore, I will pass the test.

D
The definition of a triangle is a three-sided polygon. This shape has three sides. Therefore, it is a triangle.
Solution
The correct answer is - All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

Key Points
- A categorical syllogism consists of three parts: a major premise, a minor premise, and a conclusion, all of which are categorical propositions.
- In this type of logical argument, the premises and conclusion contain subjects and predicates that state something about the categories to which things belong.
- Typically, the structure follows this format:
  
  Major premise: All A are B.
  
  Minor premise: C is A.
  
  Conclusion: Therefore, C is B.
- For example, in the provided answer:
  
  Major premise: All men are mortal.
  
  Minor premise: Socrates is a man.
  
  Conclusion: Socrates is mortal.
- This structure demonstrates a categorical syllogism by logically connecting the premises to reach a conclusion.
Additional Information
- Syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion.
- There are several types of syllogisms, including:
  
  Categorical Syllogism: Composed of categorical propositions and asserts whether something belongs to a category.
  
  Conditional Syllogism: Involves 'if-then' statements, and the conclusion is based on the condition provided in the premise.
  
  Disjunctive Syllogism: Involves either-or statements, and the conclusion is drawn based on the elimination of one option.
- Understanding the different types of syllogisms is crucial for analyzing and constructing logical arguments effectively.
Question 5
5 / -1

In this question, four statements are given followed by three conclusions. Choose the conclusion(s) which best fit(s) logically.

Statements:

1) All lions are ducks.

2) No duck is horse.

3) All horses are fruits.

4) Some horses are tanks.

Conclusions:

I. All ducks being fruits is a possibility.

II. Some tanks are lions.

III. No fruit is lion.

A
All conclusions follow

B
Only conclusion II and III follows

C
Only conclusion I and III follows

D
Only conclusion I follows

Solution

Statements:

1) All lions are ducks.

2) No duck is horse.

3) All horses are fruits.

4) Some horses are tanks.

The least possible Venn diagram:

Conclusions:

I All ducks being fruits is a possibility. - True (Because, there is no relation between ducks and fruits so it can be possible and possibility is also given)

II. Some tanks are lions. - False (Because, there is no direct relation between tanks and lions, so it can be possible but not definite)

III. No fruit is lion. - False (Because, there is no direct relation between fruit and lion, so it can be possible but not definite)

So, Only conclusion I follows.

Hence, the correct answer is "Only conclusion I follows".
Question 6
5 / -1

A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.

Main Statement:

Pradeep becomes either a Director or a Producer.

Statement P: Pradeep is a Director.

Statement Q: Pradeep is a Producer.

Statement R: Pradeep is not a Director.

Statement S: Pradeep is not a Producer.

Select the correct answer.

A
SP only

B
RQ only

C
Both SP and RQ

D
Neither SP nor RQ

Solution

Key Points

Main statement: Pradeep becomes either a Director or a Producer.

⇒ It means Pradeep cannot be both. Also, he must be one of them.

SP:

⇒ Statement S: Pradeep is not a Producer.

⇒ It means he must be a Director, as given in statement P.

⇒ So, statement P follows from S and they are logically consistent with the main statement.

RQ:

⇒ Statement R: Pradeep is not a Director.

⇒ It means he must be a Producer, as given in statement Q.

So, statement Q follows from R and they are logically consistent with the main statement.
Question 7
5 / -1

Three Statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statement I: No land is water.

Statement II: No water is air.

Statement III: No air is forest.

Conclusion I: No land is forest.

Conclusion II: Some air are water.

A
Only conclusion I follows

B
Neither conclusion I nor II follows

C
Only conclusion II follows

D
Both conclusions I and II follow

Solution

Given Statements:

No land is water.

No water is air.

No air is forest.

The least possible diagram:

Conclusion:

I: No land is forest. - False (Because, there is no direct relative between land and forest so it can be possible but not definite)

II: Some air are water. - False (Because, No water is air, so it can be possible)

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".
Question 8
5 / -1

Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:

Some beds are chairs.

Some chairs are tables.

All tables are cupboards.

Conclusions:

I. Some tables are beds.

II. Some cupboards are chairs.

III. Some cupboards are beds.

A
Only conclusion III follows.

B
Only conclusion I follows.

C
Only conclusion II follows.

D
All conclusions follow.

Solution

The least possible venn diagram can be drawn as,

Conclusions:

I. Some tables are beds → Not Follows (This is possible but not definite).

II. Some cupboards are chairs → Follows (Because all tables are cupboards, and some tables are chairs).

III. Some cupboards are beds → Not Follows (This is possible but not definite).

Hence, the correct answer is "Only conclusion II follows".
Question 9
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Two statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:

All knives are guns.

Some bullets are knives.

Conclusions:

I. Some guns are bullets.

II. No bullet is a gun.

III. Some guns are knives.

A
Both conclusions II and III follow.

B
Both conclusions I and III follow.

C
Conclusions I, II and III follow.

D
Both conclusions I and II follow.

Solution

Given Statements:

I. All knives are guns.

II. Some bullets are knives.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some guns are bullets.- True (Because those parts of guns which are knives will have bullets also).

II. No bullet is a gun - False (Because those part of guns which are knives will be bullets also).

III. Some guns are knives - True (All knives are guns, so some guns are knives)

So, Both conclusions I and III follow.

Hence, the correct answer is "Option 2".
Question 10
5 / -1

Given below are two statements:

Statement I: A syllogism in formal logic always uses deductive reasoning.

Statement II: All arguments using inductive reasoning guarantee a certain conclusion from their premises.

In the light of the above statements, choose the most appropriate answer from the options given below:

A
Both Statement I and Statement II are true

B
Both Statement I and Statement II are false

C
Statement I is true but Statement II is false

D
Statement I is false but Statement II is true
Solution
The answer is Statement I is true but Statement II is false.

Key Points

Statement I is true.
- A syllogism in formal logic is a type of argument that consists of three propositions: two premises and a conclusion.
- The conclusion of a syllogism is deduced from the premises using the rules of formal logic.
- Therefore, syllogisms always use deductive reasoning.
Statement II is false.
- Inductive reasoning is a type of reasoning that involves drawing general conclusions from a set of specific observations.
- However, inductive reasoning does not guarantee a certain conclusion from its premises.
- It is possible to draw an incorrect conclusion from a set of observations, even if the observations are accurate.
Here are some examples:
- Syllogism:
  
  All humans are mortal.
  
  Socrates is a human.
  
  Therefore, Socrates is mortal.
- This syllogism uses deductive reasoning to reach a certain conclusion. The conclusion is guaranteed to be true if the premises are true.
- Inductive reasoning:
  
  All swans I have ever seen are white.
  
  Therefore, all swans are white.
- This is an example of inductive reasoning. It is possible that there are black swans somewhere in the world, even though I have never seen one.
- Therefore, the conclusion of the inductive argument is not guaranteed to be true.