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 physics electronic devices boolean algebra digital electronics and logic gates logic gates

Which of the following is/are correctly matched to their respective statement?

  1. Distributive Law This law permits multiplying or factoring out of an expression.

  2. Double Negation Law This law allows removal of brackets from an expression and regrouping of the variables.

  3. Commutative Law The order of application of two separate terms is not important.

  4. Associative Law A term that is inverted twice is equal to the original term.
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation
According to the commutative Law,
$A+B=B+A$
$A.B=B.A$
Hence the order of application is not important.
According to the Associative Law,
$A+(B+C)=(A+B)+C$
$A.(B.C)=(A.B).C$
According to the Distributive Law,
$(A+B).(A+C)=A.A+A.C+B.A+B.C$
Hence, multiplying or factoring out is permitted.
Multiple choice mathematical modelling proof by contradiction similar triangles

Which of the following is the correct steps to take when proving a statement using proof by contradiction?

  1. 1) Assume that your statement is true.

    2) Show this is the case using definitions and theorems.

    3) State that the statement is true.

  2. 1) Assume your statement is true for a certain instance.

    2) Show that it is true in more than one instance.

    3) State that your statement must be true.

  3. 1) Assume your statement to be false.

    2) Proceed as you would in a direct proof.

    3) Come across a contradiction.

    4) Use the contradiction to state that your assumption of the statement being false can't be the case, so your statement must be true.

  4. None of the answers are correct.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Proof by contradiction can be used to prove any kind of statements.

Steps to be followed:
     $\rightarrow$ Assume the statement we want to prove to be false.
     $\rightarrow$ Then start proving from that statement. 
     $\rightarrow$ We end up seeing our assumption to be wrong.
     $\rightarrow$ Now we can conclude our statement to be true. 

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

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.