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

According to Euclid's axioms, the _____ is greater than the part.

  1. Half

  2. Large

  3. Whole

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

According to axiom $5$ of Euclid, whole is greater than the part and it is a universal truth.


Proof:
Let's take whole $3$ and part $\dfrac{1}{3}$
Subtracting, we get
$3-\dfrac{1}{3} = \dfrac{8}{3} > 0$

Hence, Proved that whole is greater than part.

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

Euclid stated that all right angles are equal to one another in the form of a/an ..........

  1. Axiom

  2. Defination

  3. Postulate

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

Postulates


1. A straight line may be drawn from any point to any other point.


2. A terminated line (line segment) can be produced indefinitely.
 3. A circle may be described with any centre and any radius.


4. All right angles are equal to one another.


5. If a straight line falling on two straight lines makes the interior angles on the same

side of it, taken together less than two right angles, then the the two straight lines if

produced indefinitely, meet on that side on which the sum of angles is taken together

less than two right angles.

Euclid used the term postulate for the assumptions that were specific to geometry

and otherwise called axioms. A theorem is a mathematical statement whose truth

has been logically established.
Answer (C) Postulate

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

_______ is another name for postulate.

  1. theorem

  2. conjectures

  3. axiom

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

A postulate is a statement that is accepted without proof. Axiom is another name for a postulate. 


For example, if you know that Pam is five feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings are at least five foot one. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.


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

A statement accepted as true as the basis for argument or inference, is

  1. Axioms

  2. Conjecture

  3. Corollary

  4. Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
A statement accepted as true as the basis for argument or inference, is axioms.

Let us consider an axiom of addition and multiplication.
Let $x$ and $y$ be real numbers.
Then $x + y$ is also a real number and $xy$ is also a real number.
Multiple choice maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

Read the following axioms:
(i) Things which are equal to the same thing are equal to one another.
(ii) If equals are added to equals, the wholes are equal.
(iii) Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.

  1. Consistent

  2. Inconsistent

  3. Either

  4. Neither
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This set of axiom is consistent.
(i) If a=b and b=c then a =c
(ii) If a = b and c = d then a+ b =c +d
(iii) If x = 2y and z = 2y then x = z

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

A proof is required for :

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

A theorem is:

  1. an assumption

  2. always true

  3. always false

  4. sometimes true and sometimes false
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A theorem is a Statement (logic) that has been proved on the basis of previously established statements, such as other theorems, and generally accepted statements.
A theorem is based on assumption that theorem is true.


Example: In a Euclidean space, the sum of measures of the three angles of any triangles is invariably equal to the straight angle, also as $180^o$

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

The converse of "if $x\in A\cap B$ then $x\in A$ and $x\in B$", is

  1. If $x\in A$ and $x\in B$, then $x\in A\cap B$.
  2. If $x\not\in A\cap B$, then $x\not\in A$ or $x\not\in B$.
  3. If $x\not\in A$ or $x\not\in B$, then $x\not\in A\cap B$.
  4. If $x\not\in A$ or $x\not\in B$, then $x\in A\cap B$.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The converse of "If P then Q" is "If Q then P"
Hence, Option A

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

  1. If you lose the game then you dont know the rules or you are overconfident.

  2. A sufficient condition that you win the game is that you know the rules or you are not overconfident.

  3. If you dont know the rules or are overconfident you lose the game

  4. If you know the rules and are overconfident then you win the game.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Contrapositive is the inverse of the converse of the statement.

It is obtained by first interchanging the hypothesis and conclusion and then adding "not" to both
In this case, converse is "If you win the game, then you know the rules but are not overconfident."
Inverse of this statement gives answer as A.

Multiple choice maths introduction of probability theory types of events some more terms in probability events and its algebra

While doing any experiment, there will be a possible outcome which is called

  1. An impossible event

  2. A sure event

  3. An exhaustive event

  4. A complementary event
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

While doing any experiment, there will be a possible outcome is called sure event.
Example: Getting $3$ of $1, 2, 3, 4, 5, 6$ in rolling die is a sure event.