Flashcards: Mathematical Reasoning | Mathematics (Maths) for JEE Main & Advanced PDF Download

 Page 1


 
 
MATHEMATICAL REASONING 
Reasoning is the basis of mathematics. When we are called upon to solve a problem, we have to follow 
the chain of reasoning and thus form one thing to other, and still from that to another, we reach the 
solution. 
This chapter introduces the art of mathematical reasoning, its precision and rigour. 
Everything has been explained in great detail to help the learner understand the basics.  
 
 
 
 
 
 
 
 
 
 
Mathematical 
Reasoning 
Inductive 
(Mathematical Induction) 
Deductive 
Page 2


 
 
MATHEMATICAL REASONING 
Reasoning is the basis of mathematics. When we are called upon to solve a problem, we have to follow 
the chain of reasoning and thus form one thing to other, and still from that to another, we reach the 
solution. 
This chapter introduces the art of mathematical reasoning, its precision and rigour. 
Everything has been explained in great detail to help the learner understand the basics.  
 
 
 
 
 
 
 
 
 
 
Mathematical 
Reasoning 
Inductive 
(Mathematical Induction) 
Deductive 
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
A sentence is called a mathematically acceptable statement which is either true or false but not both. A 
statement is an unambiguous declarative sentence which conveys a complete thought and which is either 
true or false but not both. 
Example : 
A.P.J. ABDUL KALAM WAS PRESIDENT OF INDIA. 
Mr. 'X' will qualify IIT JEE entrance exam. 
From the above two sentences, we can say first sentence is true and there is no confusion. In 
Mathematics such sentences are called 'STATEMENTS'. 
  
Page 3


 
 
MATHEMATICAL REASONING 
Reasoning is the basis of mathematics. When we are called upon to solve a problem, we have to follow 
the chain of reasoning and thus form one thing to other, and still from that to another, we reach the 
solution. 
This chapter introduces the art of mathematical reasoning, its precision and rigour. 
Everything has been explained in great detail to help the learner understand the basics.  
 
 
 
 
 
 
 
 
 
 
Mathematical 
Reasoning 
Inductive 
(Mathematical Induction) 
Deductive 
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
A sentence is called a mathematically acceptable statement which is either true or false but not both. A 
statement is an unambiguous declarative sentence which conveys a complete thought and which is either 
true or false but not both. 
Example : 
A.P.J. ABDUL KALAM WAS PRESIDENT OF INDIA. 
Mr. 'X' will qualify IIT JEE entrance exam. 
From the above two sentences, we can say first sentence is true and there is no confusion. In 
Mathematics such sentences are called 'STATEMENTS'. 
  
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
On the other hand second sentence may be true or false i.e. there is ambiguity. 
Such a sentence is not mathematically acceptable. 
Exclamatory sentence (How Sweet!), Imperative sentence (Bring a glass of water.), interrogative 
sentences (what are you doing?), sentences involving variable time such as Yesterday and Tomorrow, 
Today are not mathematically acceptable statement. Also if pronouns do not refer to a particular person 
or it involves a variable places such as here, there, etc, then such sentences are not mathematically 
acceptable statements. 
  
Page 4


 
 
MATHEMATICAL REASONING 
Reasoning is the basis of mathematics. When we are called upon to solve a problem, we have to follow 
the chain of reasoning and thus form one thing to other, and still from that to another, we reach the 
solution. 
This chapter introduces the art of mathematical reasoning, its precision and rigour. 
Everything has been explained in great detail to help the learner understand the basics.  
 
 
 
 
 
 
 
 
 
 
Mathematical 
Reasoning 
Inductive 
(Mathematical Induction) 
Deductive 
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
A sentence is called a mathematically acceptable statement which is either true or false but not both. A 
statement is an unambiguous declarative sentence which conveys a complete thought and which is either 
true or false but not both. 
Example : 
A.P.J. ABDUL KALAM WAS PRESIDENT OF INDIA. 
Mr. 'X' will qualify IIT JEE entrance exam. 
From the above two sentences, we can say first sentence is true and there is no confusion. In 
Mathematics such sentences are called 'STATEMENTS'. 
  
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
On the other hand second sentence may be true or false i.e. there is ambiguity. 
Such a sentence is not mathematically acceptable. 
Exclamatory sentence (How Sweet!), Imperative sentence (Bring a glass of water.), interrogative 
sentences (what are you doing?), sentences involving variable time such as Yesterday and Tomorrow, 
Today are not mathematically acceptable statement. Also if pronouns do not refer to a particular person 
or it involves a variable places such as here, there, etc, then such sentences are not mathematically 
acceptable statements. 
  
 
 
 
 
 
Example : 
He is an engineering graduate from IIT DELHI, IIT KHARAGPUR is away from here. Statements are 
denoted by small letters ?? , ?? , ?? , … and written as ?? : Ram is an engineer. 
  
Page 5


 
 
MATHEMATICAL REASONING 
Reasoning is the basis of mathematics. When we are called upon to solve a problem, we have to follow 
the chain of reasoning and thus form one thing to other, and still from that to another, we reach the 
solution. 
This chapter introduces the art of mathematical reasoning, its precision and rigour. 
Everything has been explained in great detail to help the learner understand the basics.  
 
 
 
 
 
 
 
 
 
 
Mathematical 
Reasoning 
Inductive 
(Mathematical Induction) 
Deductive 
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
A sentence is called a mathematically acceptable statement which is either true or false but not both. A 
statement is an unambiguous declarative sentence which conveys a complete thought and which is either 
true or false but not both. 
Example : 
A.P.J. ABDUL KALAM WAS PRESIDENT OF INDIA. 
Mr. 'X' will qualify IIT JEE entrance exam. 
From the above two sentences, we can say first sentence is true and there is no confusion. In 
Mathematics such sentences are called 'STATEMENTS'. 
  
 
 
 
 
FUNDAMENTALS OF DEDUCTIVE 
REASONING 
Statements 
On the other hand second sentence may be true or false i.e. there is ambiguity. 
Such a sentence is not mathematically acceptable. 
Exclamatory sentence (How Sweet!), Imperative sentence (Bring a glass of water.), interrogative 
sentences (what are you doing?), sentences involving variable time such as Yesterday and Tomorrow, 
Today are not mathematically acceptable statement. Also if pronouns do not refer to a particular person 
or it involves a variable places such as here, there, etc, then such sentences are not mathematically 
acceptable statements. 
  
 
 
 
 
 
Example : 
He is an engineering graduate from IIT DELHI, IIT KHARAGPUR is away from here. Statements are 
denoted by small letters ?? , ?? , ?? , … and written as ?? : Ram is an engineer. 
  
 
 
 
 
NEGATION OF A STATEMENT 
The denial of a statement is called the negation of the statement. If ?? is a statement, then the negation of 
?? is also a statement and is denoted by ~ ?? , and read as 'not ?? ' 
Example : 
?? : everyone in India speaks Hindi. 
~ ?? : everyone in India does not speak Hindi