Revision Notes: Mathematical Reasoning

# 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.
```

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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