1. STATEMENTS
Sentence which is either true or false but not both at the same time is called a
statement.
Statements are denoted by p,q,r ........
If a statement is true, its truth value is ''T" and if it is false, its truth
value is "F" Ex: p: 6 > - 4 (T)
If two or more statements combine with the connectives (or, and, if...
then, if and only if) are called compound statements.
Compound statements are Disjunction, Conjunction, Implication and
Bi-implication.
If p, q are simple statements
p v q (p or q) - Disjunction
p Λ q (p and q) - conjunction
p q (P implies q) - Implication
P q (P double implies q) - Bi-implication
• Tautologies: Some compound statements contain only 'T' in the last
column of their truth tables. Such statements are called tautologies.
Ex: p Λ (~q) p
• Contradiction: A compound statement which contains only "F" in the
last column of its truth table is called a contradiction.
Ex: p Λ (~p)
• Quantifiers: 2 types
1) Universal quantifiers 2) Existential quantifier
1) The quantifier, 'for all' or 'for every' denoted by " ", is called the
universal quantifier.
2) The quantifier 'for some' or 'there exists atleast one' is called the
existential quantifier. It is denoted by " ".
• Converse, Inverse and Contrapositive of of a Implication:
Implication : p q
Converse : q p
Inverse : ~p ~q
Contrapositive : ~q ~p