Mathematical reasoning is a vital topic in the academic course of applied mathematics. The topic is meant to benefit the students greatly in the future. Moreover, the CBSE Class 11 Applied Maths Mathematical Reasoning allows the students to understand mathematics using logic and principles. All the topics are selected by experts keeping in mind its importance in an academic career

Check out the information given below to know more about the chapter on mathematical reasoning.

  • There are a total of three topics under the applied maths mathematical reasoning portion class 11.
  • It assists students in developing critical thinking skills that aid them in approaching a problem using the logic in mathematical reasoning. 
  • The post offers detailed information regarding the topics included, important questions of specific chapters, and notes that can help the students approach the chapter of mathematical reasoning. 

What is CBSE Class 11 Applied Maths 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 that are prevalent. These are – deductive reasoning and inductive reasoning. Both of them have a specific use in the scientific world. 

With the use of mathematical reasoning, students 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.

Topics included in Mathematical & Logical Reasoning

There are a total of three topics included in the mathematical reasoning in applied mathematics class 11.

Check out the table below to know more about the topics.

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)

NCERT Solutions for CBSE Class 11 Mathematical Reasoning

Applied mathematics is a new academic course. As it is recently introduced, there are no books available yet. But, the students can refer to the CBSE class 11 applied mathematics handbook released by the board. 

Check out the applied maths mathematical reasoning class 11 pdf. 

http://cbseacademic.nic.in/web_material/Curriculum20/publication/srsec/840_APPLIED_MATHS-XI.pdf

The handbook is detailed and offers an interesting insight. The CBSE Class 11 Applied Maths Mathematical Reasoning part is explained intricately. The language is simple and concise. It reflects the knowledge of the experts and how they want the present generation to hone the necessary mathematical skills. The problems and solutions given will aid the students greatly. 

Mathematical Reasoning CBSE Class 11 Notes

Check out the applied maths mathematical reasoning class 11 notes so that you can prepare the topic easily.

Mathematical reasoning is divided into two broad categories. These are – Deductive reasoning and inductive reasoning. 

Statement

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.

Compound statement

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.

Special words/phrases

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 word “And”

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

  1. The compound statement containing "and" is false if any one of the component statements is false.
  2. 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 word “Or”

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

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

Quantifiers

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

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

Implications

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. 

Coding-Decoding

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 –

  • Letter coding
  • Number coding

In 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.

Whereas, in 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.

Odd man out 

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.

Blood relations: 

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.

Syllogism 

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.

FAQ's

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.