Conditional Statement
In the study of logic, there are two types of statements, conditional statement and biconditional statement. These statements are formed by combining two statements, which are called compound statements. Suppose a statement is if it rains, then we don’t play. This is a combination of two statements. These types of statements are mainly used in computer programming languages such as c, c++, etc. Let us learn more here with examples.
Conditional Statement Definition
A conditional statement is represented in the form of “if…then”. Let p and q are the two statements, then statements p and q can be written as per different conditions, such as;
 p implies q
 p is sufficient for q
 q is necessary for p
 p ⇒ q
Points to remember:
 A conditional statement is also called implications.
 Sign of logical connector conditional statement is →. Example P → Q pronouns as P implies Q.
 The state P → Q is false if the P is true and Q is false otherwise P → Q is true.
Truth Table for Conditional Statement
The truth table for any two inputs, say A and B is given by;
A 
B 
A→B 
T 
T 
T 
T 
F 
F 
F 
T 
T 
F 
F 
T 
Example: We have a conditional statement If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then;
 If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.
 If A is false, that is, it is not raining and B is true, that is, we did not play, still the statement is true. A is the necessary condition for B but it is not sufficient.
 If A is true, B should be true but if A is false B may or may not be true.
What is a BiConditional Statement?
A statement showing an “if and only if” relation is known as a biconditional statement. An event P will occur if and only if the event Q occurs, which means if P has occurred then it implies Q will occur and vice versa.
P ↔ Q ⇒ (P→Q) ∨ (Q→P) 
Example:
P: A number is divisible by 2.
Q: A number is even.
If P will occur then Q will occur and if Q will occur then P will occur.
Hence, P will occur if and only if Q will occur.
We can say that P↔Q.
Conditional Statement Examples
Q.1: If a > 0 is a positive number, then is a = 10 correct or not? Justify your answer.
Solution: Given, a > 0 and is a positive number
And it is given a = 10
So the first statement a > 0 is correct because any number greater than 0 is a positive number. But a = 10 is not a correct statement because it can be any number greater than 0.
Q.2: Justify P → Q, for the given table below.
P 
Q 
P → Q 
I am late 
I am on time 

I am punctual 
I am on time 
Solution: Case 1: We can see, for the first row, in the given table,
If statement P is correct, then Q is incorrect and if Q is correct then P is incorrect. Both the statements contradict each other.
Hence, P → Q = False
Case 2: In the second row of the given table, if P is correct then Q is correct and if Q is correct then P is also correct. Hence, it satisfies the condition.
P → Q = True
Therefore, we can construct the table;
P 
Q 
P → Q 
I am late 
I am on time 
F 
I am punctual 
I am on time 
T 