Mathematical Reasoning Class 11 Notes Maths

 Page 1


 
KEY POINTS
? A sentence is called a statement if it is either true or false but not 
both simultaneously. 
? The denial of a statement p is called its negation and is written 
as ~p and read as not p. 
? Compound statement is made up of two or more simple 
statements. These simple statements are called component 
statements. 
? ‘And’, ‘or’, ‘If–then’, ‘only if’ ‘If and only if’ etc. are connecting 
words, which are used to form a compound statement. 
? Two simple statements p and q connected by the word ‘and’ 
namely ‘p and q’ is called a conjunction of p and q and is written 
as p q ? .  
? Compound statement with ‘And’ is 
(a) true if all its component statements are true 
(b) false if any of its component statement is false 
p q 
p q ?
T T T 
Page 2


 
KEY POINTS
? A sentence is called a statement if it is either true or false but not 
both simultaneously. 
? The denial of a statement p is called its negation and is written 
as ~p and read as not p. 
? Compound statement is made up of two or more simple 
statements. These simple statements are called component 
statements. 
? ‘And’, ‘or’, ‘If–then’, ‘only if’ ‘If and only if’ etc. are connecting 
words, which are used to form a compound statement. 
? Two simple statements p and q connected by the word ‘and’ 
namely ‘p and q’ is called a conjunction of p and q and is written 
as p q ? .  
? Compound statement with ‘And’ is 
(a) true if all its component statements are true 
(b) false if any of its component statement is false 
p q 
p q ?
T T T 
 
T F 
F T 
F F 
F 
F 
F 
? Two simple statements p and q connected by the word ‘or’  the 
resulting compound  statement ‘p or q’ is called disjunction of p 
and q and is written as p q ? 
? Compound statement with ‘Or’ is 
(a) true when at least one component statement is true 
(b) false when both the component statements are false 
p q 
p q ?
T 
T 
F 
F 
T 
F 
T 
F 
T 
T 
T 
F 
? The negation of the compound statement ‘ p or q’ is ‘ p and q ? ? ’
( ) p q p q ? ? ? ? ? ? . 
? The negation of the compound statement ‘ p and q’ is ‘ p or q ? ? ’
( ) p q p q ? ? ? ? ? ? . 
? A statement with “If p then q” can be rewritten as 
(a) p implies q 
(b) p is sufficient condition for q 
(c) q is necessary condition for p 
Page 3


 
KEY POINTS
? A sentence is called a statement if it is either true or false but not 
both simultaneously. 
? The denial of a statement p is called its negation and is written 
as ~p and read as not p. 
? Compound statement is made up of two or more simple 
statements. These simple statements are called component 
statements. 
? ‘And’, ‘or’, ‘If–then’, ‘only if’ ‘If and only if’ etc. are connecting 
words, which are used to form a compound statement. 
? Two simple statements p and q connected by the word ‘and’ 
namely ‘p and q’ is called a conjunction of p and q and is written 
as p q ? .  
? Compound statement with ‘And’ is 
(a) true if all its component statements are true 
(b) false if any of its component statement is false 
p q 
p q ?
T T T 
 
T F 
F T 
F F 
F 
F 
F 
? Two simple statements p and q connected by the word ‘or’  the 
resulting compound  statement ‘p or q’ is called disjunction of p 
and q and is written as p q ? 
? Compound statement with ‘Or’ is 
(a) true when at least one component statement is true 
(b) false when both the component statements are false 
p q 
p q ?
T 
T 
F 
F 
T 
F 
T 
F 
T 
T 
T 
F 
? The negation of the compound statement ‘ p or q’ is ‘ p and q ? ? ’
( ) p q p q ? ? ? ? ? ? . 
? The negation of the compound statement ‘ p and q’ is ‘ p or q ? ? ’
( ) p q p q ? ? ? ? ? ? . 
? A statement with “If p then q” can be rewritten as 
(a) p implies q 
(b) p is sufficient condition for q 
(c) q is necessary condition for p 
 
(d) p only if q 
(e) (~q) implies (~p) 
? If in a compound statement containing the connective ‘‘or’’ all the 
alternatives cannot occur simultaneously, then the connecting 
word ‘‘or’’ is called as exclusive ‘‘or’’. 
? If, in a compound statement containing the connective ‘‘or’’, all 
the alternative can occur simultaneously, then the connecting 
word ‘‘or’’ is called as inclusive ‘‘or’’. 
? Contrapositive of the statement p ? q is the statement ~ q ?~p 
? Converse of the statement p ? q is the statement q ? p 
? “For all”, “For every” are called universal quantifiers 
? A statement is called valid or invalid according as it is true or 
false.