Page 13 - Chapter 2

Truth Table :

• Example p q pq

T T T
Form the implication p=>q for each T F F
the following F T T

F F T
(a) p: I am hungry. q: I will eat.
Note: p <=> q is T when p and q are both T
(b) p: 2+2=5 q: I am the king of or both F.

England.
• Example 3:
Solution
Is the following equivalence a true
(a) If I am hungry, then I will eat
statement?

(b) If 2+2=5, then I am the king of English
3>2 if and only if 0< 3 – 2
Note: There is no cause-and effect
Solution :
relationship between p and q in case (b).
And (b) is true, since 2+2=5 is false. Let p: 3>2 and q : 0< 3 – 2,

• Converse and Contrapositive since p and q are both true, we then
conclude that
If p=>q is an implication, then its
p  q is true statement.
converse is the implication q => p

• Example 4.
and its contrapositive is the implication
~ q => ~p Compute the truth table of the

E.g. Give the converse and the statement

contrapositive of the implication “If it is (p=>q)  (~q => ~p)
raining, then I get wet”
Truth Table :
Converse : If I get wet, then It is raining.
p q P=>q ~q ~p ~q=>~p (p=>q)

Contrapositive : If I do not get wet, then It (~q=>~p)
Equivalence (biconditional) T T T F F T T

T F F T F F T
If p and q are statements, the
F T T F T T T
compound statement p if and only if q,
F F T T T T T
denoted by p  q, is called an
equivalence or biconditional.