In Mathematics, Mathematical Reasoning is one of the easy topics to understand, Question is easy from this topic to solve. Every year you will get at max 1  2 questions in JEE Main and other exams, directly (as chapter weight in jee main is only 3%) but indirectly, the concept of this chapter will be involved in physics semiconductor chapter where you will learn about gates and then the use of the truth table will be handy for you which you will learn in this chapter. The easy to score fact makes this chapter important from exam point of view as you will be able to solve the question in less than a minute if you have learned the concept and will be able to score some easy marks. It will be a new chapter for the student but you will find it quite easy to learn and understand. Once you through with concepts for this concept you will be able to solve questions mostly in mind with a little bit of calculation required on paper. Overall this chapter will be short compared to other chapters.
Mathematical Reasoning helps students to develop thinking ability and help them to learn how to think mathematically and approach a problem. It teaches you how to make sense of a given thing. These learning of sensemaking can be used in the mathematical problem or can be applied in unfamiliar situations, These learning will be very helpful for future learning, to deduce the thing from top to bottom or induce some result from bottom to top.
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Start NowIf you understand this chapter well you will realize how good mathematics is and you will try to stay away from rote learning and that will help you to continue your journey with mathematics smoothly otherwise you may find mathematics frustrating in future going ahead.
1. After studying this chapter you will be comfortable with logical reasoning, deductive reasoning, and sensemaking thinking.
2. You will be able to solve questions related to logical thinking and deductive, inductive reasoning, you will feel confident about your way of thinking.
3. Since mathematical reasoning involves tautology as well as a truth table, so it will be helpful to you to understand gates in physics in semiconductor chapter, If you have studied this chapter before going to those chapter of physics.
4. And obviously, the chapter itself will help you to score some easy marks in the exam as it gets about 3% weight in jee main and you will be able to solve those questions very quickly if you have studied chapter well.
Important topics :
Statements and type of statements
Basic logical connectives, conjunction, and disjunction
Negation
Conditional statements
The contrapositive of conditional statements
The converse of conditional statements
Biconditional statements
Quantifiers
Validity of statements
Statement: A statement is a sentence which is either true or false, but not both simultaneously.
Note: No sentence can be called a statement if
(ii) It is an order or request
(iii) It is a question
(iv) It involves variable time such as ‘today’ , ‘tomorrow’ , ‘yesterday’ etc.
(v) It involves variable places such as ‘here’ , ‘there’ , ‘everywhere’ etc.
(vi) It involves pronouns such as ‘she’ , ‘he’ , ‘they’ etc.
Simple Statements: Simple statements are those which can’t be broken down into two or more sentences.
Basic logical connectives: There are many ways of combining simple statements to form new statements. The words which combine or change simple statements to form new statements or compound statements are called Connectives.
Negation: An assertion that a statement fails or denial of a statement is called the negation of the statement. The negation of a statement is generally formed by introducing the word “not” at some proper place in the statement or by prefixing the statement with “It is not the case that” or It is false that”.
Conditional Statements: if p and q are any two statements, then the compound statement “if p then q” formed by joining p and q by a connective ifthen’ is called a conditional statement or an implication and is written in symbolic form as p → q or p ⇒ q. Here, p is called the hypothesis (or antecedent) and q is called a conclusion (or consequent) of the conditional statement (p ⇒ q):
The contrapositive of a conditional statement: The statement “(~ q) → (~ p)” is
called the contrapositive of the statement p → q
The converse of a conditional statement: The conditional statement “q → p” is called the converse of the conditional statement “ p → q ”
The biconditional statement: If two statements p and q are connected by the connective ‘if and only if’ then the resulting compound statement “p if and only if q” is called a biconditional of p and q and is written in symbolic form as p ↔ q.
Quantifiers: Quantifiers are the phrases like ‘These exist’ and “for every”.
For example, There exists a triangle whose all sides are equal.
The validity of statements: Validity of a statement means checking when the statement is true and when it is not true. This depends upon which of the connectives, quantifiers, and implication is being used in the statement.
For Example, Validity of statement with ‘AND’
To show statement r : p ∧ q is true, show statement ‘p’ is true and the statement ‘q’ is true.
Mathematical Reasoning is a basic topic or you can say building block for logicalmathematical thinking development and is used in many other chapters also like semiconductors in physics, so you must be through with this chapter.
First, finish all the concept, example and questions given in NCERT Maths Book. You must be thorough with the theory of NCERT. Then you can refer to the book Algebra Arihant by Dr. SK goyal or RD Sharma or Cengage Mathematics Algebra but make sure you follow any one of these not all. Sets, Relations, and Functions are explained very well in these books and there are an ample amount of questions with crystal clear concepts. Choice of reference book depends on person to person, find the book that best suits you the best, depending on how well you are clear with the concepts and the difficulty of the questions you require. In our view, the NCERT book will be enough for this chapter.
Chapters 
Chapters Name 
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 12 

Chapter 13 

Chapter 14 

Chapter 16 
The statement is equivalent to
Directions : Question is AssertionReason type. This question contains two statements : Statement 1 (Assertion) and Statement2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Question: let be the statement " is an irrational number ", be the statemen " is a transcendental number ", and be the statement " is a rational number iff is a transcendental number ".
Statement1: is equivalent to either or .
Statement2: is equivalent to
Statement1 is true, Statement2 is false
Statement1 is false, Statement2 is true
Statement1 is true, Statement2 is true Statement2 is a correct explanation for Statement1
Statement1 is true, Statement2 is true Statement2 is not a correct explanation for Statement1
Let S be a nonempty subset of R. Consider the following statement:
P : There is a rational number such that
Which of the following statements is the negation of the statement P ?
There is a rational number such that .
There is no rational number such that .
Every rational number satisfies .
and is not rational.