B tech. Discrete mathematics (I. T & Comp. Science Engg.) Syllabus

Conditional or Implication: (If…then)
If two statements are combined by using the logical connective ‘if…then’ then the resulting statement is called a conditional statement.
If P and Q are two statements forming the implication “if P then ^{Q” then we denotes this implication} P  Q ^.

In the implication P  Q,

P is called antecedent or hypothesis Q is called consequent or conclusion.

The statement P  Q false.

is true in all cases except when P is true and Q is

The truth table for implication is as follows.

P	Q	P  Q
T T F F	T F T F	T F T T

Since conditional statement play an essential role in mathematical reasoning a variety of terminology is used to express P  Q .

1. 
   If P then Q
   
2. 
   P implies Q
   
3. 
   P only if Q
   
4. 
   Q if P
   
5. 
   P is sufficient condition for Q
   
6. 
   Q when P
   
7. 
   Q is necessary for P
   
8. 
   Q follows from P
   
9. 
   if P, Q
   
10. 
    Q unless  P