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 maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Identify the Law of Logic
$(p \vee q) \vee r \equiv p \vee (q \vee r) \equiv p \vee q \vee r$

  1. Associative law

  2. Commutative Law

  3. Involution Law

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

Associative Law

This law allows the removal of brackets from an expression and regrouping of the variables.
$(p\vee q)\vee r \equiv p \vee (q \vee r)\equiv p\vee q\vee r$

Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Identify the Law of Logic
$\sim(p \wedge q) \equiv \sim p \vee \sim q$

  1. Commutative Law

  2. DeMorgan's Law

  3. Complement Law

  4. Conditional Law
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given 
$\sim (p\wedge q)=\sim p \vee \sim q$

It is Demorgan's law 
according to the if we take transpose or negation of any quatity then all the relation get opposite

Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Identify the Law of Logic
$\sim(p \vee q) \equiv \sim p \wedge \sim q$

  1. Conditional Law

  2. Demorgan's Law

  3. Absorption Law

  4. Identity Law
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given 
$\sim (p\wedge q)=\sim p \vee \sim q$

It is Demorgan's law 
according to the if we take transpose or negation of any quatity then all the relation get opposite

Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Identify the Law of Logic
$p \rightarrow q \equiv \sim p \vee q$

  1. Idempotent Law

  2. Conditional Law

  3. Involution Law

  4. Commutative Law
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
|  $p$ |  $q$ |  $p\rightarrow q$ |  $\sim p$ |  $(\sim p)\vee q$ | | --- | --- | --- | --- | --- | |  $T$ |   $T$ |   $T$ |   $F$ |   $T$ | |   $T$ |   $F$ |   $F$ |   $F$ |   $F$ | |  $F$ |   $T$ |   $T$ |   $T$ |   $T$ | |   $F$ |   $F$ |   $T$ |   $T$ |   $T$ |
We can say that if $p$ ,then $q$ or $p$ implies $q$ .
'$\rightarrow$' is called a conditional operator.
So, the giving logical equivalence is the conditional law.
Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Let p and q be any two logical statements and $r : p \rightarrow (\sim p \vee q)$. If r has a truth value F, then the truth values of p and q are respectively

  1. F, F

  2. T, T

  3. F, T

  4. T, F
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
p q $\sim$p $\sim$ p $\vee$ q r
T T F T T
F F T T T
T F F F F
F T T T T

$\therefore$ Clearly from above able, If r has a truth value F, then the truth values of p and core T and F respectively.

Multiple choice maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Let p,q be statements. Negation of statement $p \leftrightarrow  ~ q$, is

  1. $~ q \rightarrow p$
  2. $ ~ p v q$
  3. $p \leftrightarrow q$
  4. $p \rightarrow q$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
p q ~q $p \leftrightarrow ~q$ $~(p \leftrightarrow ~q)$ $~q \rightarrow p$ $~p v q$ $p \leftrightarrow q$ $p \rightarrow q$
T T F F T T T T T
T F T T F T F F F
F T T T F T T F T
F F F F T F T T T
Multiple choice business organisation and correspondence companies act, 2013 - introduction and characteristics introduction to companies companies act, 2013 company

Choose the correct answers from the following alternatives given
Which amounts to fraud:

  1. false representation as to fact

  2. a mere opinion

  3. a statement of expression

  4. a statement of intention
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Fraud involves a false representation of fact made with the intent to deceive, whereas opinions or intentions do not generally constitute fraud in a legal sense.

Multiple choice

v. to assert something or present it as a fact

  1. postulate

  2. precedent

  3. pinnacle

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

To postulate means to suggest or assume the truth of something as a basis for reasoning or argument. Precedent and pinnacle are nouns, while pragmatic is an adjective, making postulate the only verb option.

Multiple choice

v. to provide evidence for; to back up (a claim)

  1. conventional

  2. contend

  3. convey

  4. corroborate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Corroborate means to confirm or give support to a statement, theory, or finding. Conventional is an adjective meaning standard, contend means to assert or struggle, and convey means to transport or communicate.

Multiple choice

Choose the best definition for hypothesis

  1. definition

  2. main idea

  3. data

  4. unproven explanation
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A "hypothesis" is a proposed explanation made on the basis of limited evidence as a starting point for further investigation. This matches "unproven explanation."

Multiple choice

A tentative (untested) explanation is known as?

  1. theory

  2. idea

  3. hypothesis

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

A hypothesis is a proposed, tentative explanation for a phenomenon that can be tested through further investigation and experimentation. A theory is a well-tested and widely accepted explanation, while a conclusion is the final decision reached at the end of an investigation.

Multiple choice

What is the format of a hypothesis statement?

  1. If.....then...because....

  2. I believe......

  3. I infer......

  4. I'm sure that....likey....because...
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A scientific hypothesis is typically structured as an "If... then... because..." statement to clearly link the proposed cause, the expected effect, and the underlying scientific reasoning. This format makes the hypothesis testable and easy to evaluate during an experiment.

Multiple choice

An inference is when you

  1. see something happeneing

  2. dream something is happening

  3. use clues to determine what is happening

  4. guess what is happening
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inference is using evidence and clues to draw conclusions about what is happening, even when you did not directly observe it. It is different from direct observation (seeing it happen) or random guessing.