Reader's Digest: Are you a Class 11 commerce student starting your journey of Applied Mathematical Reasoning? Read the blog on CBSE Class 11 Applied Mathematical Reasoning, exploring its fundamental concepts, dissecting the syllabus, providing valuable notes & discussing its real-world implications.

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. 

Here's a glimpse of what we'll be delving into:

• Meaning of CBSE Class 11 Applied Maths - Mathematical Reasoning - Uncovering the essence of this subject and why it's vital for your commerce education.
• Syllabus of CBSE Class 11 Applied Maths - Mathematical Reasoning - A comprehensive overview of the topics and chapters in this blog.
• CBSE Class 11 Applied Maths - Mathematical Reasoning Notes - Valuable resources and study materials to aid your understanding and performance.
• Class 11 Applied Maths - Mathematical Reasoning Implications - How mastering these mathematical reasoning skills can benefit your future academic and career pursuits.

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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: deductive reasoning and inductive reasoning. Both of them have a specific use in the scientific world. 

Using 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.

CBSE Class 11 Applied Maths - Mathematical Reasoning Syllabus

The topics covered in CBSE Class 11 Applied Mathematics enable students to use mathematical knowledge in 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.)

CBSE Class 11 Applied Maths - Mathematical Reasoning Notes

Mathematical reasoning is divided into two broad categories: deductive and inductive. It encourages students to engage in mathematical investigations and build connections within mathematical topics and other disciplines.

Check out the Mathematical Reasoning Class 11 Notes PDF to understand the topic in-depth and enhance your exam preparation.

Statement

A statement, or 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.

Read More: CBSE Class 11th Maths Syllabus

Compound Statement

Here, more than one statement is joined by words like "or", "and", etc. When two or more statements are joined to form a compound statement, each statement 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

Some words or phrases 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 unique 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, sometimes, "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

Several implications 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, q must also be true. But, there is no explanation given if p is false. Thus, if p is false, it does not affect q. 

Coding-Decoding

A code is a system of signals. Coding is essentially a method of sending and receiving messages in a form that others cannot intercept. 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 find the answer.
• Number coding: The specific letter is replaced by a number. Here, 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 quickly. The relation will be convoluted, and you must think carefully before concluding. You might have to go through several small relationships to reach the last one.

Syllogism 

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

Class 11 Mathematical Reasoning Sample Questions

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.

Check: CBSE Class 11 Applied Math Books

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, indicating 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 statements as “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.

Read More: What is the CBSE Class 11 Numerical Applications Syllabus

Conclusion

In this comprehensive exploration of CBSE Class 11 Applied Mathematical Reasoning, we've dissected the essence of this subject and its vital role in commerce education. From unravelling its meaning to delving into the syllabus, we've provided valuable notes and discussed real-world implications. Here are the key takeaways:

• Importance of Mathematical Reasoning: This subject is not just about numbers; it's about developing critical thinking skills for commerce and beyond.
• Syllabus Overview: We've given you a detailed look at the topics covered, from mathematically acceptable statements to logical reasoning problems.
• Valuable Notes: Access the Mathematical Reasoning Class 11 Notes PDF to boost your understanding and exam preparation.
• Key Concepts: Understand the fundamental concepts like statements, compound statements, special words/phrases, quantifiers, and implications.
• Sample Questions: We've provided sample questions to test your knowledge and understanding of the subject.