The document explains mathematical reasoning, which is essential for understanding mathematics and making sound judgments about statements. It defines a statement as a sentence that can be classified as true or false and discusses the concepts of negation and compound statements created using logical connectives such as 'and' and 'or'. Furthermore, it outlines how to negate statements and the truth values associated with conjunctions and disjunctions.

2.  What is Mathematical Reasoning
 Statement
 Negation Of Statement
 Compound Statement using connectives
( Conjunction , Disjunction )

3.  “ Mathematical Reasoning is the critical skill that enables
a student to make use of all other mathematical skills.
With the development of mathematical reasoning,
student recognize that mathematics makes sense and
can be understood.”

4.  Statement is sentence that can be judges as True or
False without ambiguity.
 Statement can be any types whether it is True or False.
Example: 1) The product of two positive number is positive.(True)
2) 2+2 = 5 (False)
Generally statement are denoted by small letters p , q , r,…

5. Statement should not contain following things,
 Request
 Exclamation ( ! )
 Order
 Question ( ? )
 Involving variable time( Today , Tomorrow ,Yesterday)
 Pronoun ( He , She etc. )

6. 1. Please open the door. ( Request )
2. What a beautiful house is ! ( Exclamation )
3. Get lost. ( Order )
4. What is Mathematics ? ( Question )
5. Tomorrow is holiday. ( Involving Variable time )
6. He is scientist. ( Pronoun )
are not statement.

7.  As simple meaning of Negation means Negative .
 It is denoted by symbol ~ .
 If a statement p is true, then negation of statement p is false
and vice versa.
Example :
Find the negation of the given statement,
1) 5 is odd number .
2) Mathematics is the queen of science.
Answer :
1) 5 is not odd number.
2) Mathematics is not the queen of science.

8.  When two statements p and q are combined form then it
is called as compound form .
 ‘ Or ’ and ‘ And ’ are logical connectives.
 They are used to form compound statement .

9.  Two or more simple statement are connected by ‘ And ’.
 If p and q are two statements then it can be written as ,
Notation
Example:
Ahmedabad is in Gujarat and 3 + 2 = 6.
And negation of conjunction will be disjunction.
p q

10. p q
T T T
T F F
F T F
F F F
p q
T = Truth value of true statement
F = Truth value of false statement

11.  Two or more simple statement are connected by ‘ or ’.
 If p and q are two statements , then it can be written as,
Notation:
Example:
Gujarat is a state of India or Ahmedabad is in Maharashtra.
And negation of disjunction will be conjunction.
p q

12. p q
T T T
T F T
F T T
F F F
p q
T = Truth value of true statement
F = Truth value of false statement