Go through the** important questions for class 11 Maths Chapter- 14 – Mathematical Reasoning** provided here. Solving these questions on mathematical reasoning will help you score better marks in class 11. All the types of questions are given here, such as MCQs, short answer type, long answer type, HOTS questions, Value-Based Questions are provided here with solutions. The questions are framed as per the syllabus of the CBSE board. The questions are repeatedly asked in the examinations. This chapter is the easiest one to score the marks. You can score marks by preparing the sample questions provided here. Also, get all the chapters important questions for Maths at BYJU’S.

Class 11 Maths Chapter 14 – Mathematical Reasoning covers the following important concepts such as:

- Statements
- Simple statements
- Compound statement
- Basic logical connectives
- Conjunction
- Disjunction
- Negation
- Conditional statement
- The contrapositive of the conditional statement
- The converse of the conditional statement
- Biconditional statement
- Quantifiers
- Validating the statement

**Also, Check: **

- Important 1 Mark Questions for CBSE Class 11 Maths
- Important 4 Marks Questions for CBSE Class 11 Maths
- Important 6 Marks Questions for CBSE Class 11 Maths

## Class 11 Chapter 14 – Mathematical Reasoning Important Questions with Solutions

Practice the following important questions in class 11 Maths Mathematical reasoning, which would help you everywhere. Solving these kinds of questions is the best way to learn the topic thoroughly.

**Question 1:**

Write the negation of the following statements

1) The number 3 is less than 1.

2) Every whole number is less than 0.

3) The sun is cold

**Solution:**

The negation of the given statements are:

1)The number 3 is not less than 1 (or) The number 3 is more than 1.

2) Every whole number is not less than 0 (or) Every whole number is more than 0.

3) The sun is not cold (or)The sun is hot.

**Question 2:**

Write a component statement for the following compound statements:

50 is a multiple of both 2 and 5.

**Solution: **

Given compound statement: 50 is a multiple of both 2 and 5.

p: 50 is multiple of 2

q: 50 is multiple of 5.

**Question 3:**

Identify the quantifier in the following statement.

There exists a real number which is twice itself.

**Solution:**

Given statement:

There exists a real number which is twice itself.

For the given statement, the quantifier is “**There exists**”.

**Question 4:**

Write the contrapositive of the given if-then statements:

(a) If a triangle is equilateral, then it is isosceles

(b) If a number is divisible by 9, then it is divisible by 3.

**Solution:**

(a) Given statement: If a triangle is equilateral, then it is isosceles

Contrapositive statement: If a triangle is not isosceles, then it is not equilateral.

(b) Given statement: If a number is divisible by 9, then it is divisible by 3.

Contrapositive statement: If a number is not divisible by 3, then it is not divisible by 9.

**Question 5:**

Show that the statement, p: if a is a real number such that a^{3} + 4a =0, then a is 0″, is true by direct method?

**Solution:** Let q and r are the statements given by q: a is a real number such that a^{3} + 4a =0

r: a is 0.

let q be true then

a is a real number such that a^{3} + 4a =0

a is a real number such that a(a^{2} + 4) =0

a = 0

r is true

So, q is true and r is true, so p is true.

**Question 6:**

Find the component statements for the following given statements and check whether it is true or false:

(a) A square is a quadrilateral and its four sides are equal

(b) All prime numbers are either even or odd

**Solution:**

**(a) **Given statement: A square is a quadrilateral and its four sides are equal

The component statements are:

P: A square is a quadrilateral

Q: A square has all its sides equal.

In this statement, the connecting word is “**and**”

We know that a square is a quadrilateral

So, the statement P is true.

Also, it is known that all the four sides of a square are equal.

Hence, the statement “Q” is also true.

Therefore, both the component statements are true.

**(b) **Given statement: All prime numbers are either even or odd

The component statements are:

P: All the prime numbers are odd numbers

Q: All the prime numbers are even numbers

In this statement, the connecting word is** “or”**

We know that all the prime numbers are not odd numbers

So, the statement P is false.

Also, it is known that all the prime numbers are not even numbers.

Hence, the statement “Q” is also false.

Therefore, both the component statements are not true.

**Question 7: **

Which of the following sentences are statements? Justify your answer.

(i) Answer this question

(ii) All the real numbers are complex numbers

(iii) Mathematics is difficult

**Solution:**

Given:

(i) Answer this question

Since it is an order, the given sentence is not a statement.

(ii) All the real numbers are complex numbers

We know that all the real numbers can be written in the form: a+i0

Where a is a real number. Hence, it always true, the given sentence is a statement

(iii) Mathematics is difficult

Mathematics is a subject that can be easy for some people and difficult for some people.

So, the given sentence can be both true or false.

Hence, it is not a statement.

### Practice Problems for Class 11 Maths Chapter 14 – Mathematical Reasoning

Solve and practice the given below problems:

- Verify by the method of contradiction that √
*7*is irrational. - Check whether the following statement is true or not: “if a and b are odd integers, then ab is an odd integer”
- Check the validity of the following statement: “square of the integer is positive or negative.”
- Write the contrapositive for the following statement: if a is a prime number, then a is odd.
- Write the negation of the given statement: All students live in dormitories.
- Show that the following statement is true by method of contra positive: ‘If x is an integer and x² is even, then x is also even’.
- Write the negation of the following statements:

(i) p: For every positive real number x, the number x-1 is also positive.

(ii) q: All cats scratch

(iii) r: For every real number x, either x>1 or x<1.

(iv) s: There exists a number x such that 0<x<1.

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