Important Questions for Class 11 Maths Chapter 14 Mathematical Reasoning

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Important Questions for Class 11 Maths Chapter 14 Mathematical reasoning are covered in this article. The chapter explains that in a scientific investigation or assertion, logic is not only based on a single person's opinion. A factual and scientific foundation is required for derivations and proofs. Mathematical Logical reasoning and critical thinking are essential skills for solving maths reasoning problems.

Very Short Answer Questions [1 Mark Questions]

Ques. Consider the following sequence: 12, 10, 13, 11, 14, 12, ... What should be the next number?

13
15
16
10

Ans. Option d) 10

Hint: 2 is deducted first, then 3 is added, resulting in 15 when 3 is added to 12. This is an example of a subtraction series with alternating numbers.

Ques. Which one of the following statements is true?

I'll leave tomorrow
She'll arrive today.
The number 3 is a prime number.
It's Friday tomorrow.

Ans. Option c) The number 3 is a prime number.

Hint: The statement that “The number 3 is a prime number” is correct because A statement is a sentence which is either true or false at the same time, but not both are true and false.

Ques. A % B, means divide

A $ B, means subtract

A @ B, means add

A # B, means multiply then,

70 $ 30 @ 80 % 20 # 10 =?

60
80
20
10

Ans. Option b) 80

Hint: Firstly, here ‘%’, ‘$’, ‘@’, ‘#’ symbol represents that division, subtraction, addition, multiplication respectively then,

70 - 30 + 80 / 20 x 10 = 80

Ques. CIRCLE: CIRCUMFERENCE:: SQUARE:?

RADIUS
CHORD
SECTOR
PERIMETER

Ans. Option d) PERIMETER

Hint: The perimeter of a square determines its boundary, just as the circumference of a circle determines its boundary.

Ques. If (a and b) is true then

a is false and b is true
a is true and b is true
a is true and b is false
all of the above

Ans. d) all of the above

Hint: (a and b) are false when both a and b are false otherwise it is true.

Ques. In the following statement, find the quantifier.

There exists a whole number that is thrice of itself.

Ans. The Given statement: There exists a whole number that is thrice of itself.

"There exists" is the quantifier for the given sentence.

Ques. Which of the following statements is a conjunction?

Shyam and Ram are friends
Both Shyam and Ram are friends
Both Shyam and Ram are enemies
All of the above

Ans. d) All of the above

Hint: All of the sentences are conjunctions. Hence, the option d is the right answer.

Short Answer Questions [2 Marks Questions]

Ques. For the below given statements, write a compound statement: 40 is divisible by both 4 and 10.

Ans. Given the compound statement: 40 is divisible by both 4 and 10.

p: 40 is divisible of 4.

q: 40 is divisible of 10.

Ques. In logic, what is the difference between a statement and a sentence?

Ans.

Statement: A statement is a sentence which is either true or false at the same time, but not both are true and false.

Sentence: If a sentence contains an exclamation, an order, a request, a question, or represents time, location, or pronouns, it is not regarded as a Statement.

Ques. For the given if-then statements, write the contrapositive statement.

If a triangle is equilateral, then all of its angles are 60°
If a number is multiple of 9, then it is multiple of 3.

Ans.

Given statement: If a triangle is equilateral, then all of its angle is 60°.

Contrapositive statement: If all the angles of a triangle is not 60°, then it is not equilateral.

Given statement: If a number is multiple of 3, then it is multiple of 9.

Contrapositive statement: If a number is not a multiple of 3, then it is not a multiple of 9.

Ques. Which of the sentences below is a statement? Justify your response.

Complex numbers are all real numbers.
Maths is a difficult subject.

Ans. Given:

Complex numbers are all real numbers.

We already know that all real numbers may be expressed as a+i0, where a is a real number. As a result, the given sentence is always true, and it is a statement.

Mathematics is a difficult subject.

Mathematics is a subject which can be simple for some and challenging for others. As a result, the above sentence could be true or false.

Hence, it is not a statement.

Ques. By using the direct approach, prove that the statement p: if x is a real number such that x3 + 4x =0, then a is 0′′ is true.

Ans. Let a and b be the statements given by

a: x is a real number such that x³ + 4x is equal to 0.

b: x is equal to 0.

If a is true, then x is a real number such that x3 + 4x = 0.

x is a real number such that x (x² + 4) =0.

x = 0

Therefore, b is true Since a and b are both true, p is also true.

Long Answer Questions [3 Marks Questions]

Ques. Write the negation of the sentences below.

The number 4 is always less than 1.
All real numbers are less than 0.
The moon is hot.

Ans. The negation of the above given statements are as follows:

The number 4 is not less than 1 or the number 4 is greater than 1.
No real number is less than 0 or every whole number is greater than 0.
The moon is not hot or the moon is hot.

Ques. Given 3 examples for sentences which are not statements. Give reasons for the following statements.

Ans.

"Rashi is a beautiful girl" is not a statement. This statement is dependent on one's point of view. Rashi may appear attractive to certain individuals, but she may not appear attractive to others. As a result, we cannot clearly conclude that the sentence is true.
"Open the door" is not a statement. It's just a sentence that gives someone instructions. There's no doubt about whether it's true or false.
"Yesterday was Tuesday" is not a statement. This sentence is only true if it is said on Wednesday, and it is false if it is said on any other day of the week. The true or false of a statement is determined by the moment it is said, not by mathematical reasoning.

Ques. For the following statement write the negation.

Bangalore is the capital of Tamil Nadu.
I was present in the class yesterday.
Tomorrow my sister is going to America.

Ans.

Bangalore is not the capital of Tamil Nadu.
I was not present in the class yesterday.
Tomorrow my sister is not going to America.

Very Long Answer Questions [5 Marks Questions]

Ques. Check whether the following statements are true or false and identify the component statements.

A rectangle is a quadrilateral and its adjacent sides are equal.
All the prime numbers are either odd or even.

Ans.

Given statement: A rectangle is a quadrilateral and its adjacent sides are equal.

The compound statements are:

p: A rectangle is a quadrilateral.

q: A rectangle adjacent sides equal.

The connecting word in this phrase is "and." As we all know that a rectangle is a quadrilateral. Hence the statement p is true.

In addition, the adjacent sides of a rectangle are known to be equal.

Hence, the statement q is also true. So, both of the compound statements are true.

Given statement: All the prime numbers are either odd or even.

The compound statements are:

p: All the prime numbers are even numbers

q: All the prime numbers are odd numbers.

The connecting word in this phrase is "or." We know that none of the prime numbers are odd. As a result, the statement p is false.

It is also well known that all prime numbers are not even. As a result, the statement q is also false.

Hence, neither of the compound statements is true.

Ques. Make five different versions of the following sentence that all convey the same concept.

p: An obtuse-angled triangle is formed when a triangle is equiangular.

Ans. The following is a list about how to write the provided statement in 5 different ways:

"A triangle is only equiangular if it has an obtuse angle."
"A triangle is not an equiangular triangle if it is not an obtuse-angled triangle."
"For a triangle to be obtuse-angled, equi angularity is a sufficient condition."
"An obtuse angle is an essential requirement for a triangle to be equiangular."
"If a triangle is equiangular, it is obtuse-angled."

Ques. Write the converse and contrapositive of each of the following sentences.

If x is a prime number, it is an odd number.
The two lines do not intersect in the same plane if they are parallel.
To say something is cold means it has a low temperature.
If you don't know how to reason deductively, you won't be able to understand geometry.
Because x is an even number, it is divisible by four.

Ans.

The contrapositive of the following statement: If x is not an odd number, it is not a prime number.

The converse of the following statement: If x is an odd number, it is a prime number.

The contrapositive of the following statement: They are not parallel if two lines intersect in the same plane.

The converse of the following statement Parallel lines are those that do not intersect in the same plane.

The contrapositive of the following statement: It is not cold if anything does not have a low temperature.

The converse of the following statement: It is cold if anything is at a low temperature.

The contrapositive of the following statement: You can understand geometry if you know how to reason deductively.

The converse of the following statement: You won't be able to understand geometry if you don't know how to reason deductively.

The contrapositive of the following statement: If x is an even number, it can be divided by 4.

The converse of the following statement: If x can be divided by 4, it is an even number.

Mathematics Related Links:
Math MCQs	Permutation and Combination	Mensuration
Trigonometry	Number Systems	Arithmetic
Probability and Statistics	Algebra	Difference Between in Math
Maxima and Minima	Symmetric and Skew Symmetric Matrices	Tautology
Cartesian System	Radical	Asymptotes

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