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 mathematical modelling proof by contradiction similar triangles

To prove any preposition by "giving counter example" we must give at-least ______ example(s).

  1. One

  2. Two

  3. Three

  4. more than three
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
In order to prove any given statement wrong, we need to specify atleast one example against that example.

Hence, to prove any preposition by "giving counter example" we must give at least ONE example.
Multiple choice mathematical modelling proof by contradiction similar triangles

The proposition $(p \, \Rightarrow \, ~p)\,\wedge \, (~p \, \Rightarrow  \, p)$ is a

  1. Tautology

  2. neither tautology nor contradiction

  3. contradiction

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
p ~p $P\Rightarrow   ~P$ $~P\Rightarrow P$ $(P\Rightarrow ~P)\wedge (~P\Rightarrow P)$
T F  F   T                    F
F T  T F F
Multiple choice mathematical modelling proof by contradiction similar triangles

Which of the following is true for counter example.

  1. A counter example is an exception to a proposed general rule or law

  2. A counter example is a specific instance of the falsity of a universal quantification (a "for all" statement).

  3. Any hard-working student is a counter example to "all students are lazy"

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

All three a,b,c are true

A counter example is an exception to a proposed general rule or law is a defination.Counterexamples are often used in math to prove the boundaries of possible theorems.option C is an example of counterexample and option b and option a are more or less same

Multiple choice text document and word processing introduction to word visual communication information communication technology (ict) physics

Closed word assumption says.

  1. If a proposition cannot be proved it is assumed to be false

  2. If a proposition is always false

  3. If a proposition is always true

  4. If a proposition cannot be prove it is assumed to be true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Closed World Assumption in logic states that any statement that cannot be proven true within the system is assumed to be false.

Multiple choice introduction of business laws business law and contract act business studies

ad volorem menas

  1. According to value

  2. To the same thing

  3. To infinity

  4. Hear the other side
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ad valorem is Latin for 'according to value,' referring to taxes or fees proportional to an item's worth (e.g., property tax, customs duty). Unlike specific taxes (fixed per unit), ad valorem varies with the assessed value. The question has a spelling error: 'ad volorem' should be 'ad valorem.'

Multiple choice classification of computer introduction to the information age physics

Certainly factor is defined as __________________.

  1. Major of belief-major of disbelief

  2. Major of disbelief-major of belief

  3. Major of evidence-major of belief

  4. Major of belief=major of evidence
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In expert systems and fuzzy logic, the Certainty Factor (CF) is calculated as the measure of belief (MB) minus the measure of disbelief (MD).

Multiple choice biology the living world botanical gardens, zoological parks and zoological museums museums and zoos tools of taxonomy

.......... are devices consisting of a series of contrasting or contradictory statements or propositions requiring the identifier to make comparisons and decisions.

  1. Herbarium

  2. Taxonomic keys

  3. Monograph

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Taxonomic keys are written characteristic information that helps a person to identify an unknown species of living organism. The taxonomic key provides a certain structure on the basis of which the user can sort out the taxonomic position of the unknown species.

Taxonomic keys are devices consisting of a series of contrasting or contradictory statements or propositions requiring the identifier to make comparisons and decisions.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$(p \wedge \sim q)\wedge (\sim p \vee q)$ is

  1. tautology

  2. contradiction

  3. dualoty

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

Evaluating the expression using truth tables or logical equivalences shows that it evaluates to false for all truth values of the variables. The components simplify such that a proposition and its negation are strictly contradicted, yielding a contradiction.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

Which of the following is not correct ?

  1. $p \vee \sim p $ is a tautology.
  2. $\sim (\sim p) \leftrightarrow p$ is a tautology.
  3. $p \wedge \sim p $ is a contradiction.
  4. $([(p \wedge p ) \rightarrow q] \rightarrow p)$ is a tautology.
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

$\because [(p \wedge p ) \rightarrow q ] \rightarrow p \equiv ( p

\rightarrow q ) \rightarrow p   (\because p \wedge p \equiv p)$

when $p$ is false and $q$ is true (or false) then

$(p \rightarrow q) $ is true i.e. $(p \rightarrow q ) ]\rightarrow p$ is false

Hence $[(p \wedge p ) \rightarrow q] \rightarrow p$ is not a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

Which of the following statement is a tautology?

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

$\because (\sim p  \vee \sim q) \vee (p  \vee \sim q) $

$\equiv (\sim p \vee p ) \vee (p \vee \sim q )$    (by distributive law)

$ \equiv t \vee \sim q \equiv t $                      t is a tautology

Hence $(\sim p  \vee \sim, q ) \vee (p  \vee \sim q )$ is a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$ p\Rightarrow p \vee q$ is

  1. a tautology.

  2. a contradiction.

  3. a tautology and a contradiction.

  4. neither a tautology nor a contradiction.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$p$       $q$      $p\vee q$       $p\rightarrow (p\vee q)$
T T     T            T
T F    T            T
F T    T              T
F F     F            T

Since, all the entries in the last column has true value. So, the given statement is a tautology

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$p\Rightarrow \sim p$ is

  1. a tautology.

  2. a contradiction.

  3. a tautology and a contradiction.

  4. neither a tautology nor a contradiction.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
 $p$  $\sim p$  $p\Rightarrow \sim p$
 T  F  F
 F  T  T

So the result of the Truth table show that $p\Rightarrow \sim p$ is neither a tautology not a contradiction

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

$ p\wedge  (\sim p)$ is

  1. a tautology.

  2. a contradiction.

  3. a tautology and a contradiction.

  4. neither a tautology nor a contradiction.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Truth table is,

$p$         $\sim p$ $p\wedge (\sim p)$
T                      F                      F
F T F

Hence given statement is contradiction.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

Which of the following is a contradiction?

  1. $p\vee q$
  2. $p\wedge q$
  3. $p\vee (\sim p)$
  4. $p\wedge (\sim p)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$p$  $q$  $p\vee q$  $p\wedge q$
$ T$ $ T$ $ T$ $ T$
$ T$ $ F$ $ T$ $ F$
$ F$ $T$ $T$ $F$
$ F$ $F$ $ F$ $ F$
So $p\vee q$ and $p\wedge q$ are not contradiction 

Now check other options:

| $p$ |  $\sim p$ |  $p\vee (\sim p)$ |  $p\wedge (\sim p)$ | | --- | --- | --- | --- | |  $T$ | $ F$ | $ T$ | $ F$ | | $ F$ | $T$ | $T$ | $F$      |
Hence $p\wedge (\sim p)$ is contradiction 

Note: If a compound statement is always False , then it is called contradiction