Conditional Statement

In mathematics, a conditional statement is a logical statement with the form “if p then q”. Here, p is the hypothesis and q is the conclusion. In conditional statements, the statement is false only when p is true and q is false, otherwise the conditional statement is usually true. The related form of conditional statement is contrapositive, which means if not q then not p.


The conditional statement is symbolically written as:
p → q

We can follow the below mentioned steps to write a conditional statement. 


Step 1: Look out for the condition that has the ‘if’ and ‘then’ part. 

Step 2: The next step is to connect the condition with the consequence by using the ‘if… then…’ structure.

Step 3: Write a statement expressing logical relationship to connect the condition and consequence.

 

For example, 

• True statements:
  
  If the square of a number is even, then the number is even. 
   

• False statements: 
  
  If a number is odd, then it is prime

To fully grasp conditional statements, students must understand their components. The parts of conditional statements are mentioned below:
 

• Hypothesis
• Conclusion

To understand the parts of the conditional statement, let us use an example

Conditional statement: If it is Friday today, then yesterday was Thursday.

Hypothesis: "If today is Friday". The hypothesis always begins with “if.”

Conclusion: The conclusion in the same example is, “then yesterday was Thursday.” Remember that the conclusion always starts with the word ‘then.’

The statement will be changed to either of the following if there is a change of order in the statement:

• Converse Statement
• Inverse Statement
• Contrapositive Statement
• Biconditional Statement 

We use the concept of conditional statements in various fields and applications. Let us now see how conditional statements are used in real world applications.
 

• Computer Science and Programming:

We use conditional statements in computer science and programming for if-else statements, which are used to control the flow of programs, we also use conditional statements to make decisions based on conditions in algorithms.

• Mathematics and Logic:

In mathematics and logic, conditional statements are used in proofs, theorems, and set theory, where they are used for finding conditional relationships between subsets.

• Engineering and Automation:

We use conditional statements in engineering and automation, where we use conditional statements to operate automated machines which operate based on conditional logic; we also use conditional statements for the functioning of traffic lights. For example, if the light is red, then cars must stop; if it is green, then cars may go.