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 introduction to euclid's geometry euclid's fifth postulate conditional statements and converse euclid's postulates

State true or false:

Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles

this the fifth postulate,many tried to prove it but at the end they had to assume something which was very closely related to the fifth postulate,they didnot form any new geometries but from where they started they ended at the same point.
$B$

Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

A proof is required for a :

  1. Postulate

  2. Axiom

  3. Theorem

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

Axiom/Postulate — a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved. 


Theorem — a mathematical statement that is proved using rigorous mathematical reasoning.  In a mathematical paper, the term theorem is often reserved for the most important results.

So, the correct option is $C$ as a theorem needs a proof.

Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

The formation or expression of an opinion or theory without sufficient evidence for proof is known as

  1. axioms

  2. conjecture

  3. corollary

  4. theorem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The formation or expression of an opinion or theory without sufficient evidence for proof is known as conjecture.

For example, make a conjecture about the next number in the pattern $2, 6, 11, 17, ...$. The terms increase by $4$, then $5$, and then $6$.
Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

__________ implies to conclude or suppose from grounds or evidence insufficient to ensure reliability.

  1. axioms

  2. conjecture

  3. corollary

  4. theorem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Conjecture implies to conclude or suppose from grounds or evidence insufficient to ensure reliability.

For example, make a conjecture about the next number in the pattern 2 ; 6 ; 11 ; 17 ; ... The terms increase by 4, then 5, and then 6.
Multiple choice maths axioms, postulates and theorems euclid's fifth postulate conditional statements and converse euclid's postulates

What is a conjecture?

  1. A true statement

  2. A statement that you believe is true based upon your observations

  3. A proven statement about something you believe

  4. A statement used by scientists
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formation or expression of an opinion or theory without sufficient evidence for proof is known as conjecture. 


Or a conjecture can be stated as a statement that you believe is true based upon your observations.

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

Select the correct statement:

  1. Normative statements can be challenged with evidence.

  2. Normative statement deals with ought to be situation.

  3. Positive statement deals with should be situation.

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

A normative statement expresses a value judgment or an opinion about what ought to be, whereas a positive statement describes what is and can be tested with evidence.

Multiple choice business economics and quantitative methods nature and scope of economics definition, scope, importance and limitation of statistics introduction - statistics for economics meaning and definition of statistics

Which of the following sentence shows distrust about statistics?

  1. There are three types of lies-lies,damn lies and statistics.

  2. Figures do not lie; liars make figure.

  3. It can prove anything.

  4. All of above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

All three statements are related to a major limitation of statistics which is "improper use of statistics". There is a vast scope for error in the data and it may be misused by people with agendas, these people may manipulate the data to gain favour or popularity. 

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

Solve it:-
$\left( {p \to q} \right) \to [\left( { \sim p \to q} \right) \to q]$

  1. Tautology

  2. Contradiction

  3. Contingent

  4. Not statement
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$Y=\left( p\longrightarrow q \right) \longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$
Method : TRUTH TABLE [  ALWAYS PREFERABLE]

 $p$  $q$  $p\longrightarrow q$  $\left( \sim p\longrightarrow q \right) $  $\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$  $Y$
 $1$  $0$  $0$  $1$  $1$ $1$ 
 $1$  $1$  $1$  $1$  $1$  $1$
 $0$  $0$  $1$  $0$  $1$  $1$
 $0$  $1$  $1$  $1$  $1$  $1$
As the result is always TRUE $\left(i.e. 1\right)$;
$\left( p\longrightarrow q \right)\longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$ is Tautology.

A. Tautology



















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

Let $p$ and $q$ be two propositions given by
$p$ : The sky is blue.
$q$ : The milk is white.
Then $p\wedge q$ will be

  1. The sky if blue or milk is white

  2. The sky is blue and milk is white

  3. The sky is white and milk is blue

  4. If the sky is blue then milk is white
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$p \wedge q$ means statement p and q
=> The sky is blue and  milk is white.

Multiple choice business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

Negation of $(\sim p\rightarrow q)$ is ________________.

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

The negation of an implication (p -> q) is (p AND NOT q). Applying this to (~p -> q), we get (~p AND NOT q), which simplifies to (~p AND ~q).

Multiple choice business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$p$: He is hard working.
$q$: He is intelligent.
Then $ \sim q\Rightarrow\sim p$, represents

  1. If he is hard working, then he is not intelligent.

  2. If he is not hard working, then he is intelligent.

  3. If he is not intelligent, then he is not had working.

  4. If he is not intelligent, then he is hard working.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

p:she is hardworking
q:she is intelligent

~p:she is not hardworking
~q:she is not intelligent

~q=>~p means She is not intelligent implies she is not hardworking
Hence, Option C

Multiple choice business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$p:$ He is hard working.
$q:$ He will win.
The symbolic form of "If he will not win then he is not hard working", is

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

Given $p:$ He is hard working

and $q:$ He will win
we get $\sim p:$ He is not hard working

and $\sim q:$ He will not win
Now the given statement in the question is "If he will not win then he is not hard working" which means 
"If he will not win then he is not hard working"
For this conditional statement, the symbolic form is $\left( \sim q \right) \Rightarrow \left( \sim p \right) $