This document discusses logical conditionals. It defines implication (conditional) as two statements connected by "if p, then q" and represented by p → q. Implication is true except when the antecedent (p) is true and consequent (q) is false. Bi-conditional is defined as two statements connected by "p if and only if q" and represented by p ↔ q. It is true except when one statement is true and the other false. Examples of implication and bi-conditional are provided along with their truth tables.

2. We have to learn:
 Implication or Conditional
 Bi-Conditional
 Some Example

3. Implication
 Two Simple statement p and q connected by the phrase
‘ if p , then q ’ is called Implication or Conditional of p and
q statements .
 It is represented by p q
Example :
1) If an integer is divisible by 9 , then the sum of its digits
is divisible by 9.
2) If the roads are wet , then it has rained .

4. Expression of Implication
1. If p then q.
2. q , if p.
3. p only if q.
4. p is sufficient condition for q .
5. q is necessary condition for p .
p is called the hypothesis or antecedent.
q is called the conclusion or consequent.

5. Truth value of Implication
p q
T T T
T F F
F T T
F F T
p q
T = Truth value of true statement
F = Truth value of false statement

6. Bi-Conditional
 Two Simple statement p and q connected by the phrase
‘ p if and only if q ’ is called Bi-conditional of p and q statements .
 It is represented by p q p q q pOr and
Example :
p : Quadrilateral ABCD is a rectangle .
q : Quadrilateral ABCD is a square .
Biconditional :
Quadrilateral ABCD is a rectangle if and only if
it is a square .

7. Truth value of Bi-conditional
p q
T T T
T F F
F T F
F F T
p q
T = Truth value of true statement
F = Truth value of false statement

8. Thank
You