Page 6 - Chapter 2

 Propositional variables • Conjunction

In logic, the letters p, q, r … denote If p and q are statements, the

propositional variables, which are conjunction of p and q is the
replaced compound statement “p and q”

by statements denoted by p∧ q .

p: 1+2 = 5 Truth Table :
q: It is raining. p q p V q

 Compound statements T T T
T F T
Propositional variables can be
F T T
combined by logical connectives to F F F

obtain compound statements. E.g. Note : p∧ q is T if and only if p is T and

p and q : 1+2 =5 and it is raining. q is T.

 Negation (a unary operation) • Example
If p is a statement, the negation of p is
Form the conjunction of p and q
the statement not p, denoted by ~ p, p: 1>3 q: It is raining.
meaning “it is not the case that p”.

if p is true, then ~p is false, and if p is Solution: p∧ q : 1 > 3 and It is
false, then ~p is true. raining.

Truth Table : List the truth value of a Note:
compound statement in terms of its In logic, unlike in everyday English,

component parts. we may join two totally unrelated
p ~q statements by logical connectives.

T F • Disjunction
F T
If p and q are statements, the
 Example
disjunction of p and q is the
Give the negation of the following compound statement “p or q”,

statements denoted by p V q
(a) p: 2+3 >1 Truth Table :

(b) q: It is snowing. p q p V q

Solution: T T T

(a) ~p: 2+3 is not greater than 1, T F T

namely, 2+3 <=1 F T T
(b) ~q: It is not the case that it is F F F

snowing. More simply, ~q: It is not Note: p V q is F is and only if q is F and q is F.

snowing.