Reasoning

Logic and Fallacies

1,803 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 logical equivalence mathematical logic discrete mathematics business maths maths

The proposition $(p\rightarrow \sim p)\wedge (\sim p\rightarrow q)$ is

  1. a tautology

  2. a contradiction

  3. neither a tautology nor a contradiction

  4. a tautology and a contradiction
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$p$      $q$      $\sim p$      $p\rightarrow \sim p$     $\sim p \rightarrow q$     $(p\rightarrow \sim p)\wedge(\sim p\rightarrow q)$
T T    F      F       T         F
T F    F      F       T         F
F T    T      T       T         T
F F    T      T       F         F
Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

The statement $(p-q)\rightarrow [(\sim p \rightarrow q)\rightarrow q]$ is 

  1. a tautology
  2. equivalent to $\sim p \rightarrow q$
  3. equivalent to $p\rightarrow \sim q$

  4. a fallacy
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The statement (p -> q) -> ((~p -> q) -> q) is a tautology. It can be verified using a truth table or logical equivalences.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

Which of the following proposition is a contradiction?

  1. $(\sim p\vee \sim q)\vee (p\vee \sim q)$
  2. $(p\rightarrow q)\vee (p\wedge \sim q)$
  3. $(\sim p\wedge q)\wedge (\sim q)$
  4. $(\sim p\wedge q)\vee (\sim q)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Contradiction is a preposition which is always false(F).
Here $\sim \equiv negation$ and $\wedge \equiv AND$
Let $ x=(\sim p \wedge q) \wedge (\sim q)$
If $p=F$ and $q=F$ then $x=F$
If $p=F$ and $q=T$ then $x=F$
If $p=T$ and $q=F$ then $x=F$
If $p=T$ and $q=T$ then $x=F$
Hence option (c) is correct

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$p,q,r$ are $3$ statement such that $(p\rightarrow q)\wedge (q\rightarrow r)\Rightarrow (p\rightarrow r)$ is 

  1. Tautology

  2. Contradiction
  3. $P\wedge q$
  4. $p\wedge (\sim q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression (p -> q) ^ (q -> r) -> (p -> r) is the Law of Hypothetical Syllogism, which is a fundamental tautology in propositional logic.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$p,q,r$ are $3$ statement such that $(p \rightarrow q)\wedge (q \rightarrow r)\Rightarrow (P \rightarrow r)$ is

  1. Tautology

  2. Contradiction
  3. $P \wedge q$
  4. $p \wedge (\sim q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is identical to the previous question; the expression (p -> q) ^ (q -> r) -> (p -> r) is a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

Which of the following is a tautology?

  1. $p\wedge (\sim p)$
  2. $p\wedge c$
  3. $p\vee t$
  4. $p\wedge p$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A tautology is a compound statement that is always true regardless of the truth values of its components. For option C, the disjunction of any proposition p with a true statement t always results in true, satisfying the definition of a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

The only statement among the followings that is a tautology is

  1. $A\vee(A\wedge B)$
  2. $[A\wedge (A\rightarrow B)]\rightarrow B$
  3. $B\rightarrow [A\wedge (A\rightarrow B)]$
  4. $A\wedge (A\vee B)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Option B represents modus ponens, which is a universally valid argument form and thus a tautology. By constructing a truth table, we find that the conditional statement always evaluates to true.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$p,q,r$ are $3$ statements such that $\left(p\rightarrow q\right)\wedge \left(q\rightarrow r\right)=Rightarrow \left(p\rightarrow r\right)$ is

  1. $Tautology$
  2. $Contradiction$
  3. $P\wedge q$
  4. $p\wede(\sim q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression (p -> q) ^ (q -> r) -> (p -> r) is a classic logical law known as the Hypothetical Syllogism. A truth table shows that it evaluates to True for all possible truth values of p, q, and r, making it a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

If p, q two propositions then $(p \vee \sim q) \wedge ( \sim p \wedge q)$ is

  1. a tautology

  2. a contradiction

  3. neither a tautology nor a contradiction

  4. both a tautology and a contradiction
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Analyzing the expression reveals an internal contradiction because it forces both p and not p to be true simultaneously. Therefore, the entire conjunction is always false, making it a contradiction.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

The only statement among the following taht is a tautology is -

  1. $A\wedge (A\vee B)$
  2. $A\vee (A\wedge B)$
  3. $[A\wedge (A\rightarrow B)]\rightarrow B$
  4. $B\rightarrow [A\wedge (A\rightarrow B)]$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option C represents the standard logical rule of detachment, or modus ponens, which is a tautology. Evaluating its truth table yields true in every row.