March 3, 2022

Mathematical reasoning is a vital topic in the academic course of applied mathematics. The CBSE Class 11 Applied Maths Mathematical Reasoning lets you understand the topics using logic and principles.

The topics covered under the applied maths mathematical reasoning class 11 assist students in developing critical thinking skills that aid them in approaching a problem using the logic in mathematical reasoning.

This post offers detailed information regarding the topics included, important questions of specific chapters, and notes that can help the students approach the chapter on mathematical reasoning.

Mathematical reasoning is a sub-genre of mathematics that focuses on determining the truth values of statements. There are mainly two types of mathematical reasoning: deductive reasoning and inductive reasoning. Both of them have a specific use in the scientific world.

With the use of mathematical reasoning, you can recognize the problems and think of strategies to solve them. Also, they come to logical conclusions based on logic and rules. It is precisely why the mathematics reasoning in applied mathematics class 11 CBSE is so crucial.

The topics covered in **CBSE Class 11 Applied Mathematics** enable students to use mathematical knowledge in the field of business, economics, and social sciences. There are a total of three topics included in the mathematical reasoning in applied mathematics class 11** **as tabulated below:

Topic name |

Mathematically acceptable statements |

Connecting words/ phrases in mathematical statement consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through a variety of examples related to real life and mathematics |

Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism, etc) |

Mathematical reasoning is divided into two broad categories namely deductive reasoning and inductive reasoning. It encourages students to engage in mathematical investigations and to build connections within mathematical topics and with other disciplines. Check out the **Mathematical Reasoning Class 11 Notes PDF **to understand the topic in-depth and enhance your exam preparation.

A statement, or more precisely, a mathematical statement, is the basic unit of mathematical reasoning. The statements in mathematics are not ambiguous and are either true or false. There is no place for confusion or maybe in mathematics. In short, a mathematical statement cannot be both true and false.

Statements not accepted in mathematics –

- When there is a question involved
- When the statement ends with an exclamation mark
- When the statement contains variable time
- When the statement is an order or request

Statements are denoted by small letters such as p, q, r, etc.

Here, more than one statement is joined by using words like "or", "and", etc. When two or more statements are joined to form a compound statement, each of the statements is called a component statement. If the statements "p" and "q" are joined to produce a compound statement, then the component statements are p and q, respectively.

There are some words or phrases that have a special place in mathematical reasoning. Some of these words are – And, Or, etc. These words are also called connectives. Each of them has a special role.

The rules regarding the word “And” in mathematical reasoning are -

- The compound statement containing "and" is false if any one of the component statements is false.
- The compound statement containing “and” is true if all the component statements are true.

Also, in some cases, "and" is not used to connect sentences. It cannot be termed as a connective.

The rules regarding the word “Or” in mathematical reasoning are -

- The compound statement containing “or” is false if both the component statements are false.
- The compound statement containing "or" is true if both the component statements are true, or any one of the component statements is true.

In mathematical reasoning, there are two quantifiers – “For all” and “There exists”

Each has a specific meaning that imparts great importance to a statement.

There are several implications that are found in mathematical reasoning. Some of these include – "if and only if", "if-then", "only if". Each makes a statement different when added to it.

In the case of "if-then", the statement becomes – if p then q

Now, you can deduce that if p is true, then q must also be true. But, there is no explanation given if p is false. Thus, if p is false, it has no effect on q.

A code is basically a system of signals. Coding is essentially a method of sending and receiving messages in a form that cannot be intercepted by others. It makes the information more secure.

There are two types of coding as explained below:

**Letter coding:**a specific letter in a word is substituted by another letter according to a particular rule. The main objective is to identify the coding pattern and then find the answer.**Number coding:**the specific letter is replaced by a number. Here also, the main aim is to recognize the coding pattern and answer the question.

The odd man out is a relatively easy concept. You will be given a group of items, and all you have to do is pick the one which is the most dissimilar. Remember to take a close look and not rush before answering.

In this section, you have to conclude the relationship asked. But, it will not be presented in an easy way. The relation provided will be convoluted, and you have to think carefully before reaching a conclusion. You might have to go through several small relationships to come to the last one.

A syllogism is a form of a logical and valid argument, which applies deductive reasoning. By considering two more ideas or assumptions, you can reach a specific conclusion.

**Q) **State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

(i) Sun rises or Moon sets.

(ii) To apply for a driving license, you should have a ration card or a passport.

(iii) All integers are positive or negative.

**Solution**

(i) It is not possible for the Sun to rise and the Moon to set together. Hence, the ‘or’ in the given statement is exclusive.

(ii) Since a person can have both a ration card and a passport to apply for a driving license. Hence, the ‘or’ in the given statement is inclusive.

(iii) Since all integers cannot be both positive and negative. Hence, the ‘or’ in the given statement is exclusive.

**Q)** Rewrite the following statement with “if-then” in three different ways conveying the same meaning.

*If a natural number is odd, then its square is also odd.*

**Solution:**

(i) A natural number is odd only if its square is odd.

(ii) For a natural number to be odd, it is necessary that its square is odd.

(iii) A natural number is odd indicates that its square is odd.

**Q)** Write the contrapositive and converse for the following statement

If *x* is a prime number, then *x* is odd.

**Solution**

The contrapositive of the given statement is: If a number x is not odd, then x is not a prime number.

The converse of the given statement is as follows: If a number x is odd, then it is a prime number

**Q) **Write each of the following statement in the form “if-then”

A quadrilateral is a parallelogram if its diagonals bisect each other.

**Solution**

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram

Frequently Asked Questions

Why is mathematical reasoning included within the applied mathematics academic course?

Mathematical reasoning is included within the applied mathematics academic course because of its practicality. It enables the students to approach mathematics with logic and principles. They can then solve the problem with various strategies and come to a logical conclusion.

Now, students can use mathematical reasoning to solve real-life problems. The chapters have also been carefully selected by experts. The main aim is to ensure that the students opting for commerce or art streams can also apply the basic rules of mathematical reasoning in their selected field of study.

What was the need for introducing applied mathematics as an elective course?

The introduction of applied mathematics as an elective course came as a suggestion from Dr. Ramesh Pokhriyal “Nishank”, the present Minister of Education. The subject was previously in the CBSE curriculum as a skill subject. Now, its upliftment towards being an elective academic course is a wise decision.

The idea of introducing applied mathematics as an elective subject was mainly to benefit the students opting for commerce or arts. The board observed that the knowledge they needed was different from those of the science students. Now, the students of these streams can use basic mathematical tools to solve real-world problems.

Can mathematical reasoning help students in the future?

Yes, mathematical reasoning can help students in the future. In fact, they can even use knowledge to solve real problems. Also, if you are opting for a career in fields other than pure science, sufficient knowledge regarding mathematical reasoning will help you.

Furthermore, several competitive examinations like JEE has a special part that is dedicated to mathematical reasoning. By strengthening your base and solving questions repeatedly, you can easily gain a good score in that section.

Is mathematical reasoning easy?

There is no definite answer to this particular question. It is because the question of whether or not mathematical reasoning is easy depends entirely on an individual. Some find it easy, while others find it quite hard.

However, with repeated practice and a strong foundation, you will come to find it easy in the future. The most vital aspect is to make sure that you have a clear understanding of the subject and then proceed to solve the questions given.

What is the best way to prepare for mathematical reasoning?

The best way to prepare for mathematical reasoning is to refer to the handbook that is published by CBSE. It is vital to keep into account that applied mathematics is a recently introduced academic course for session 2020-21. As such, there are no books available in the market yet.

Updated On : March 3, 2022

Mathematical reasoning is a vital topic in the academic course of applied mathematics. The CBSE Class 11 Applied Maths Mathematical Reasoning lets you understand the topics using logic and principles.

The topics covered under the applied maths mathematical reasoning class 11 assist students in developing critical thinking skills that aid them in approaching a problem using the logic in mathematical reasoning.

This post offers detailed information regarding the topics included, important questions of specific chapters, and notes that can help the students approach the chapter on mathematical reasoning.

Mathematical reasoning is a sub-genre of mathematics that focuses on determining the truth values of statements. There are mainly two types of mathematical reasoning: deductive reasoning and inductive reasoning. Both of them have a specific use in the scientific world.

With the use of mathematical reasoning, you can recognize the problems and think of strategies to solve them. Also, they come to logical conclusions based on logic and rules. It is precisely why the mathematics reasoning in applied mathematics class 11 CBSE is so crucial.

The topics covered in **CBSE Class 11 Applied Mathematics** enable students to use mathematical knowledge in the field of business, economics, and social sciences. There are a total of three topics included in the mathematical reasoning in applied mathematics class 11** **as tabulated below:

Topic name |

Mathematically acceptable statements |

Connecting words/ phrases in mathematical statement consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through a variety of examples related to real life and mathematics |

Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism, etc) |

Mathematical reasoning is divided into two broad categories namely deductive reasoning and inductive reasoning. It encourages students to engage in mathematical investigations and to build connections within mathematical topics and with other disciplines. Check out the **Mathematical Reasoning Class 11 Notes PDF **to understand the topic in-depth and enhance your exam preparation.

A statement, or more precisely, a mathematical statement, is the basic unit of mathematical reasoning. The statements in mathematics are not ambiguous and are either true or false. There is no place for confusion or maybe in mathematics. In short, a mathematical statement cannot be both true and false.

Statements not accepted in mathematics –

- When there is a question involved
- When the statement ends with an exclamation mark
- When the statement contains variable time
- When the statement is an order or request

Statements are denoted by small letters such as p, q, r, etc.

Here, more than one statement is joined by using words like "or", "and", etc. When two or more statements are joined to form a compound statement, each of the statements is called a component statement. If the statements "p" and "q" are joined to produce a compound statement, then the component statements are p and q, respectively.

There are some words or phrases that have a special place in mathematical reasoning. Some of these words are – And, Or, etc. These words are also called connectives. Each of them has a special role.

The rules regarding the word “And” in mathematical reasoning are -

- The compound statement containing "and" is false if any one of the component statements is false.
- The compound statement containing “and” is true if all the component statements are true.

Also, in some cases, "and" is not used to connect sentences. It cannot be termed as a connective.

The rules regarding the word “Or” in mathematical reasoning are -

- The compound statement containing “or” is false if both the component statements are false.
- The compound statement containing "or" is true if both the component statements are true, or any one of the component statements is true.

In mathematical reasoning, there are two quantifiers – “For all” and “There exists”

Each has a specific meaning that imparts great importance to a statement.

There are several implications that are found in mathematical reasoning. Some of these include – "if and only if", "if-then", "only if". Each makes a statement different when added to it.

In the case of "if-then", the statement becomes – if p then q

Now, you can deduce that if p is true, then q must also be true. But, there is no explanation given if p is false. Thus, if p is false, it has no effect on q.

A code is basically a system of signals. Coding is essentially a method of sending and receiving messages in a form that cannot be intercepted by others. It makes the information more secure.

There are two types of coding as explained below:

**Letter coding:**a specific letter in a word is substituted by another letter according to a particular rule. The main objective is to identify the coding pattern and then find the answer.**Number coding:**the specific letter is replaced by a number. Here also, the main aim is to recognize the coding pattern and answer the question.

The odd man out is a relatively easy concept. You will be given a group of items, and all you have to do is pick the one which is the most dissimilar. Remember to take a close look and not rush before answering.

In this section, you have to conclude the relationship asked. But, it will not be presented in an easy way. The relation provided will be convoluted, and you have to think carefully before reaching a conclusion. You might have to go through several small relationships to come to the last one.

A syllogism is a form of a logical and valid argument, which applies deductive reasoning. By considering two more ideas or assumptions, you can reach a specific conclusion.

**Q) **State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

(i) Sun rises or Moon sets.

(ii) To apply for a driving license, you should have a ration card or a passport.

(iii) All integers are positive or negative.

**Solution**

(i) It is not possible for the Sun to rise and the Moon to set together. Hence, the ‘or’ in the given statement is exclusive.

(ii) Since a person can have both a ration card and a passport to apply for a driving license. Hence, the ‘or’ in the given statement is inclusive.

(iii) Since all integers cannot be both positive and negative. Hence, the ‘or’ in the given statement is exclusive.

**Q)** Rewrite the following statement with “if-then” in three different ways conveying the same meaning.

*If a natural number is odd, then its square is also odd.*

**Solution:**

(i) A natural number is odd only if its square is odd.

(ii) For a natural number to be odd, it is necessary that its square is odd.

(iii) A natural number is odd indicates that its square is odd.

**Q)** Write the contrapositive and converse for the following statement

If *x* is a prime number, then *x* is odd.

**Solution**

The contrapositive of the given statement is: If a number x is not odd, then x is not a prime number.

The converse of the given statement is as follows: If a number x is odd, then it is a prime number

**Q) **Write each of the following statement in the form “if-then”

A quadrilateral is a parallelogram if its diagonals bisect each other.

**Solution**

If the diagonals of a quadrilateral bisect each other, then it is a parallelogram

Frequently Asked Questions

Why is mathematical reasoning included within the applied mathematics academic course?

Mathematical reasoning is included within the applied mathematics academic course because of its practicality. It enables the students to approach mathematics with logic and principles. They can then solve the problem with various strategies and come to a logical conclusion.

Now, students can use mathematical reasoning to solve real-life problems. The chapters have also been carefully selected by experts. The main aim is to ensure that the students opting for commerce or art streams can also apply the basic rules of mathematical reasoning in their selected field of study.

What was the need for introducing applied mathematics as an elective course?

The introduction of applied mathematics as an elective course came as a suggestion from Dr. Ramesh Pokhriyal “Nishank”, the present Minister of Education. The subject was previously in the CBSE curriculum as a skill subject. Now, its upliftment towards being an elective academic course is a wise decision.

The idea of introducing applied mathematics as an elective subject was mainly to benefit the students opting for commerce or arts. The board observed that the knowledge they needed was different from those of the science students. Now, the students of these streams can use basic mathematical tools to solve real-world problems.

Can mathematical reasoning help students in the future?

Yes, mathematical reasoning can help students in the future. In fact, they can even use knowledge to solve real problems. Also, if you are opting for a career in fields other than pure science, sufficient knowledge regarding mathematical reasoning will help you.

Furthermore, several competitive examinations like JEE has a special part that is dedicated to mathematical reasoning. By strengthening your base and solving questions repeatedly, you can easily gain a good score in that section.

Is mathematical reasoning easy?

There is no definite answer to this particular question. It is because the question of whether or not mathematical reasoning is easy depends entirely on an individual. Some find it easy, while others find it quite hard.

However, with repeated practice and a strong foundation, you will come to find it easy in the future. The most vital aspect is to make sure that you have a clear understanding of the subject and then proceed to solve the questions given.

What is the best way to prepare for mathematical reasoning?

The best way to prepare for mathematical reasoning is to refer to the handbook that is published by CBSE. It is vital to keep into account that applied mathematics is a recently introduced academic course for session 2020-21. As such, there are no books available in the market yet.