Logic Questions and Answers

Q: If the distance between city P and city Q is x km. and the distance between city Q and city R is y km, then the distance between city P and city R is

The distance between P and R is less than or equal to x + y.Going from P to R through Q covers x + y km, and a direct route can never be longer than a route through an intermediate point. This is the triangle inequality: PR ≤ PQ + QR. Equality holds only when Q lies on the straight line between P and R.The distance is not always exactly x + y, because Q need not lie between P and R, and it can never be greater than x + y. Since 'less than or equal to x + y' is always true, 'None of the above' is wrong too.

Q: If 'man' is called 'woman', 'woman' is called 'boy', 'boy' is called 'girl', 'girl' is called 'pilot' and 'pilot' is called 'child', then who will fly the aeroplane ?

The aeroplane will be flown by the Child.An aeroplane is flown by a pilot. In this code, 'pilot' is called 'child', so the person who flies the aeroplane is called child.The trap is to answer 'Pilot': in the code, 'girl' is called 'pilot', so 'Pilot' would name a girl. 'Girl' in the code means a boy, and 'Man' is not used as a code name for anyone.

Q: If it rains at night, then the next morning is always cloudy. The morning today is cloudy. Then

The valid conclusion is that it may have rained last night.The rule is 'if it rains at night, the next morning is cloudy'. A cloudy morning is the consequence, not the cause; mornings can be cloudy for other reasons. Reasoning from the consequence back to the cause ('the morning is cloudy, so it rained') is the fallacy of affirming the consequent, so it cannot be said that it must have rained. But a cloudy morning is consistent with rain, so rain last night remains possible.The statements say nothing about tonight, so both 'It will rain tonight' and 'It will not rain tonight' are unsupported.

Q: Whichever book Mr. A reads, Mr. B also reads that book. Whichever book Mr. B reads, Mrs. C also reads that book. Which of the following must be true ?

The statement that must be true is Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.Every book A reads, B reads, and every book B reads, C reads. So every book A has read, C has also read. If C has not read a book, A cannot have read it, which is the contrapositive of that chain; the third statement is therefore certain.The others reverse the direction of the rule. B not reading a book says nothing about C, who may read books B has not. B reading Harry Potter does not mean A did, and C reading all of Coelho does not mean A did, because the rule carries books only from A to B to C, not back.

Q: Read these six conditional claims :1. If it's an apple, then it's a fruit.2. If it's a fruit, then it's an apple.3. It's an apple if it's a fruit.4. It's a fruit if it's an apple.5. It's not a fruit if it's not an apple.6. It's not an apple if it's not a fruit.Out of these six conditional claims which three claims have the answer as Yes ?

The three true claims are 1, 4, 6.Every apple is a fruit, but not every fruit is an apple. So any claim equivalent to ‘if apple, then fruit’ is true, and any claim equivalent to ‘if fruit, then apple’ is false.Claim 1 says if apple, then fruit: true.Claim 4, ‘fruit if apple’, says the same thing: true.Claim 6, ‘not an apple if not a fruit’, is the contrapositive of claim 1: true.Claims 2 and 3 both say if fruit, then apple: false. Claim 5, ‘not a fruit if not an apple’, is the contrapositive of that false claim, so it is false too.Every other option includes at least one of claims 2, 3 or 5.

Q: Which of the following statements follows logically from the statement “India will talk, only if the terrorists are handed over” ?

The statement that follows is India will talk implies the terrorists are handed over.‘P only if Q’ means that P cannot happen without Q, that is, if P then Q. Here P is 'India will talk' and Q is 'the terrorists are handed over', so talking implies the hand-over has happened.'The terrorists are handed over, hence India will talk' reverses the condition (Q, so P), which 'only if' does not promise.'India will not talk implies that the terrorists have not been handed over' (not P, so not Q) is equivalent to that same reversal.'India will talk though the terrorists are not handed over' directly contradicts the statement.

Q: Which of the following WFFs is valid (tautology) in predicate logic ?∀x(P(x) → Q(x)) → (∃xP(x) → ∃xQ(x))

The formula is always valid.Suppose the antecedent holds, so every object with P also has Q, and suppose there is some object with P. Call it a. Then P(a) is true, so by the first assumption Q(a) is true, and therefore some object has Q.\[ \begin{aligned} &\forall x(P(x) \to Q(x)),\ P(a) \\ &\Rightarrow Q(a) \Rightarrow \exists x\, Q(x) \end{aligned} \]The argument uses no property of the domain, so the formula is true in every interpretation, finite or infinite; 'valid only for finite domains' is therefore wrong. Option B confuses the formula with its antecedent: the implication as a whole holds even when P(x) → Q(x) fails for some x, because the implication is then trivially true. ∃x(¬Q(x) &and; P(x)) is the negation of ∀x(P(x) → Q(x)), not an equivalent of the formula.

Q: A hill always has

A hill always has height.A hill is by definition a raised landform, higher than the land around it, so elevation is the one feature every hill must have.Trees, animals and water are often found on hills, but a bare, rocky or dry hill is still a hill, so none of them is essential.Questions of this kind ask for the feature that belongs to the very definition of the thing, not one that is merely common; height is part of what makes land a hill.

Q: A mirror always

A mirror always reflects.A mirror is a smooth, highly polished surface whose essential property is to reflect light, so that images are formed. Every mirror, plane, concave or convex, works by reflection.Refraction, the bending of light as it passes from one medium into another, is how lenses work. Distortion happens only with curved or uneven mirrors, not always, and 'retracts' has nothing to do with light.

Q: Choose the most meaningful sequence for the following words. 1. Job 2. Independence 3. Study 4. Income 5. Exam

Correct answer: 3, 5, 1, 4, 2The sequence follows the natural order of cause and effect. Study comes first, then the exam that tests it, then the job the qualification obtains, then the income the job brings, and finally the independence the income makes possible. Each step is the precondition of the one after it.

Important Instructions

31.

If the distance between city P and city Q is x km. and the distance between city Q and city R is y km, then the distance between city P and city R is

A.x + y
B.greater than x + y
C.less than or equal to x + y
D.None of the above

Exam Year(s)

MPPSC State Service - 2023, MPPSC Forest Service - 2023,

Answer: C

The distance between P and R is less than or equal to x + y.

Going from P to R through Q covers x + y km, and a direct route can never be longer than a route through an intermediate point. This is the triangle inequality: PR ≤ PQ + QR. Equality holds only when Q lies on the straight line between P and R.

The distance is not always exactly x + y, because Q need not lie between P and R, and it can never be greater than x + y. Since 'less than or equal to x + y' is always true, 'None of the above' is wrong too.

Discuss in Forum

32.

If 'man' is called 'woman', 'woman' is called 'boy', 'boy' is called 'girl', 'girl' is called 'pilot' and 'pilot' is called 'child', then who will fly the aeroplane ?

A.Pilot
B.Girl
C.Child
D.Man

Exam Year(s)

MPPSC State Service - 2023, MPPSC Forest Service - 2023,

Answer: C

The aeroplane will be flown by the Child.

An aeroplane is flown by a pilot. In this code, 'pilot' is called 'child', so the person who flies the aeroplane is called child.

The trap is to answer 'Pilot': in the code, 'girl' is called 'pilot', so 'Pilot' would name a girl. 'Girl' in the code means a boy, and 'Man' is not used as a code name for anyone.

Discuss in Forum

33.

If it rains at night, then the next morning is always cloudy. The morning today is cloudy. Then

A.It must have rained last night.
B.It may have rained last night.
C.It will rain tonight.
D.It will not rain tonight.

Exam Year(s)

Punjab Civil Service - 2018,

Answer: B

The valid conclusion is that it may have rained last night.

The rule is 'if it rains at night, the next morning is cloudy'. A cloudy morning is the consequence, not the cause; mornings can be cloudy for other reasons. Reasoning from the consequence back to the cause ('the morning is cloudy, so it rained') is the fallacy of affirming the consequent, so it cannot be said that it must have rained. But a cloudy morning is consistent with rain, so rain last night remains possible.

The statements say nothing about tonight, so both 'It will rain tonight' and 'It will not rain tonight' are unsupported.

Discuss in Forum

34.

Whichever book Mr. A reads, Mr. B also reads that book. Whichever book Mr. B reads, Mrs. C also reads that book. Which of the following must be true ?

A.Mr. B has not read the Shiva trilogy. So Mrs. C could not have read it.
B.Mr. B has read the Harry Potter series. So Mr. A must have read it.
C.Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.
D.Mrs. C has read all the books written by Paulo Coelho. Mr. A must have read all of those as well.

Exam Year(s)

Punjab Civil Service - 2018,

Answer: C

The statement that must be true is Mrs. C has not read the autobiography of Mahatma Gandhi. Mr. A could not have read it either.

Every book A reads, B reads, and every book B reads, C reads. So every book A has read, C has also read. If C has not read a book, A cannot have read it, which is the contrapositive of that chain; the third statement is therefore certain.

The others reverse the direction of the rule. B not reading a book says nothing about C, who may read books B has not. B reading Harry Potter does not mean A did, and C reading all of Coelho does not mean A did, because the rule carries books only from A to B to C, not back.

Discuss in Forum

35.

Read these six conditional claims :

1. If it's an apple, then it's a fruit.
2. If it's a fruit, then it's an apple.
3. It's an apple if it's a fruit.
4. It's a fruit if it's an apple.
5. It's not a fruit if it's not an apple.
6. It's not an apple if it's not a fruit.

Out of these six conditional claims which three claims have the answer as Yes ?

A.2, 3, 5
B.2, 3, 4
C.3, 4, 5
D.1, 4, 6

Exam Year(s)

Punjab Civil Service - 2021,

Answer: D

The three true claims are 1, 4, 6.

Every apple is a fruit, but not every fruit is an apple. So any claim equivalent to ‘if apple, then fruit’ is true, and any claim equivalent to ‘if fruit, then apple’ is false.

Claim 1 says if apple, then fruit: true.
Claim 4, ‘fruit if apple’, says the same thing: true.
Claim 6, ‘not an apple if not a fruit’, is the contrapositive of claim 1: true.
Claims 2 and 3 both say if fruit, then apple: false. Claim 5, ‘not a fruit if not an apple’, is the contrapositive of that false claim, so it is false too.

Every other option includes at least one of claims 2, 3 or 5.

Discuss in Forum

36.

Which of the following statements follows logically from the statement “India will talk, only if the terrorists are handed over” ?

A.The terrorists are handed over, hence India will talk.
B.India will not talk implies that the terrorists have not been handed over.
C.India will talk though the terrorists are not handed over.
D.India will talk implies the terrorists are handed over.

Exam Year(s)

Punjab Civil Service - 2021,

Answer: D

The statement that follows is India will talk implies the terrorists are handed over.

‘P only if Q’ means that P cannot happen without Q, that is, if P then Q. Here P is 'India will talk' and Q is 'the terrorists are handed over', so talking implies the hand-over has happened.

'The terrorists are handed over, hence India will talk' reverses the condition (Q, so P), which 'only if' does not promise.
'India will not talk implies that the terrorists have not been handed over' (not P, so not Q) is equivalent to that same reversal.
'India will talk though the terrorists are not handed over' directly contradicts the statement.

Discuss in Forum

37.

Which of the following WFFs is valid (tautology) in predicate logic ?

∀x(P(x) → Q(x)) → (∃xP(x) → ∃xQ(x))

A.Valid only for finite domains
B.Valid only if P(x) → Q(x) holds for every x in the domain
C.Always valid
D.Equivalent to ∃x(¬Q(x) ∧ P(x))

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

The formula is always valid.

Suppose the antecedent holds, so every object with P also has Q, and suppose there is some object with P. Call it a. Then P(a) is true, so by the first assumption Q(a) is true, and therefore some object has Q.

\[ \begin{aligned} &\forall x(P(x) \to Q(x)),\ P(a) \\ &\Rightarrow Q(a) \Rightarrow \exists x\, Q(x) \end{aligned} \]

The argument uses no property of the domain, so the formula is true in every interpretation, finite or infinite; 'valid only for finite domains' is therefore wrong. Option B confuses the formula with its antecedent: the implication as a whole holds even when P(x) → Q(x) fails for some x, because the implication is then trivially true. ∃x(¬Q(x) ∧ P(x)) is the negation of ∀x(P(x) → Q(x)), not an equivalent of the formula.

Discuss in Forum

38.

A hill always has

A.Trees
B.Animals
C.Water
D.Height

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: D

A hill always has height.

A hill is by definition a raised landform, higher than the land around it, so elevation is the one feature every hill must have.

Trees, animals and water are often found on hills, but a bare, rocky or dry hill is still a hill, so none of them is essential.

Questions of this kind ask for the feature that belongs to the very definition of the thing, not one that is merely common; height is part of what makes land a hill.

Discuss in Forum

39.

A mirror always

A.Reflects
B.Retracts
C.Distorts
D.Refracts

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: A

A mirror always reflects.

A mirror is a smooth, highly polished surface whose essential property is to reflect light, so that images are formed. Every mirror, plane, concave or convex, works by reflection.

Refraction, the bending of light as it passes from one medium into another, is how lenses work. Distortion happens only with curved or uneven mirrors, not always, and 'retracts' has nothing to do with light.

Discuss in Forum

40.

Choose the most meaningful sequence for the following words.

1. Job

2. Independence

3. Study

4. Income

5. Exam

A.1, 4, 2, 3, 5
B.2, 5, 3, 1, 4
C.3, 1, 2, 4, 5
D.3, 5, 1, 4, 2

Answer: D

Correct answer: 3, 5, 1, 4, 2

The sequence follows the natural order of cause and effect. Study comes first, then the exam that tests it, then the job the qualification obtains, then the income the job brings, and finally the independence the income makes possible. Each step is the precondition of the one after it.

Discuss in Forum

Loading…

Topics

Other Subjects

Tags: Logic Questions and Answers || Logic MCQ Questions and Answers || Logic GK Questions and Answers || Logic GK MCQ Questions || Logic Multiple Choice Questions and Answers || Logic GK || GK on Logic || Reasoning Questions and Answers || Reasoning MCQ Questions and Answers || Reasoning GK Questions and Answers || GK on Reasoning

Logic Questions and Answers

Important Instructions

Topics

Other Subjects

About Us

Stay informed about all important Dates & Notifications