Reasoning

Logic and Fallacies

1,716 Questions

Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.

Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts

Logic and Fallacies Questions

Multiple choice

The problems 3-SAT and 2-SAT are

  1. both in P

  2. both NP-complete

  3. NP-complete and in P respectively

  4. undecidable and NP-complete respectively
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

3 SAT problem is both NP & NP hard so it is NP complete, but 2 SAT problem is solvable in Polynomial time so it is in class P.

Multiple choice

Consider the following logic program P A(x) <- B(x, y), C(y) <- B(x,x) Which of the following first order sentences is equivalent to P?

  1. (∀x)[(∃y)[B(x,y)∧C(y)]⇒A(x)]∧¬(∃X)[B(x,x)]

  2. (∀x)[(∀y)[B(x,y)∧C(y)]⇒A(x)]∧¬(∃X)[B(x,x)]

  3. (∀x)[(∃y)[B(x,y)∧C(y)]⇒A(x)]∨¬(∃X)[B(x,x)]

  4. (∀x)[(∀y)[B(x,y)∧C(y)]⇒A(x)]∧(∃X)[B(x,x)]
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The logic program has two rules: A(x) if B(x,y) and C(y); and C(y) if B(x,x) with negation. The first rule translates to: for all x, if there exists y such that B(x,y) and C(y), then A(x). The second rule C(y) means y is such that NOT exists x with B(x,x). These must be combined with OR because the second rule has no body - it's a fact. Option C correctly uses OR to combine the universal quantification with the negation.

Multiple choice

The following resolution rule is used in logic programming. Derive clause (P ∨ Q) from clauses (P ∨ R), (Q ∨ ¬R) Which of the following statements related to this rule is FALSE?

  1. ((P ∨ R) ∧ (Q ∨ ¬R)) ⇒ (P ∨ Q) is logically valid

  2. (P ∨ Q) ⇒ ((P ∨ R)) ∧ (Q ∨ ¬R)) is logically valid

  3. (P ∨ Q) is satisfiable if and only if (P ∨ R) ∧ (Q ∨ ¬R) is satisfiable

  4. (P ∨ Q) ⇒ FALSE if and only if both P and Q are unsatisfiable
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If P = True, Q = False, R = True Then, we find (T$\cup F$)$\Rightarrow$(T$\cup$T) $\land$(F$\cup$F) T$\Rightarrow$(T$\land$F) T$\Rightarrow$F F$\cup$F False is not valid.

Multiple choice

Directions: In the following question, an incomplete statement is provided. Select the option which most logically completes the idea in the question statement.

The realm of infinity has been explored by physicists and mathematicians alike but ________________.

  1. both have discovered the true secret

  2. they have been painfully unsuccessful at it

  3. they have not fully understood it

  4. the casual factors have never led themselves to subjugation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Look at the keyword explored and but. Due to appearance of but as a connect, we must have some idea in second part of sentence opposite to explored, which can aptly be found in option (3).

Multiple choice

Which of the following is correct?

  1. Rebuttable presumption arises that a man is alive if it is shown that he was alive within thirty years.

  2. Rebuttable presumption arises that a man is dead if it is proved that he has not been heard of for seven years by those who would naturally have heard from him if he had been alive.

  3. Both (1) and (2)

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option C is correct. Option A is correct - Section 107 of the Evidence Act provides that when a person was alive within 30 years, there is a rebuttable presumption that he is alive. Option B is also correct - Section 108 provides that when a person has not been heard of for 7 years by those who would naturally have heard, there is a rebuttable presumption that he is dead. Both presumptions are provided by law, so 'Both (1) and (2)' is the correct answer. Both are rebuttable with evidence.

Multiple choice

Directions: In the following question, four statements are provided. These statements form a coherent paragraph when properly arranged. Select the alternative representing the proper and logical sequencing of these statements.

A. There would be no point in our trying to go into the various so called ‘Theories of Truth’ that have been produced and upheld by various philosophers. B. This attempt has in fact given rise to many well–known puzzles and many of them have arisen because of the number of different sorts of assertions that we should normally be prepared to call true or false, to which it is hard to say what sort of facts would correspond. C. There is just one of them that is worth mentioning here, the one which is known as the Correspondence Theory, according to which an assertion is true if, and only if, it corresponds to a fact.
D. This theory is worth mentioning because it arises precisely out of an attempt to build the everyday association between ‘truth’ and ‘fact’ into a systematic and consistent way of thought.

  1. CABD

  2. ACDB

  3. CDBA

  4. BDCA
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This para jumble explains one 'theory of truth' in philosophical aspect. Thus, it begins with A, supported by C that names the theory. As D explains the theory, it follows C.

Multiple choice

A hypothesis being confirmed by numerous tests is known as

  1. an opinion

  2. an assumption

  3. a theory

  4. speculation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If after repeated testing and peer review by other scientists in the same field, an hypothesis still holds up as a valid explanation for a group of facts, it becomes accepted as a theory.

Multiple choice

Evidence is of two types,

  1. oral evidence and documentary evidence

  2. general evidence and special evidence

  3. physical evidence and non-physical evidence

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Evidence is of two types: oral evidence and documentary evidence.