IF THEN STATEMENT

If-Then Statement

Definition Of If-Then Statement

If-then statement is a conditional statement in the form If A, then B, where A is a hypothesis and B is a conclusion. An if-then statement is used in deductive reasoning.

Example of If-then Statement

If two rays have a common vertex, then they form an angle.
If two lines intersect, then their intersection is a point.

Video Examples: Geometry: If-Then Statements

Solved Example on If-then Statement

Ques: Identify the if-then form of the given statement. A regular polygon has all its sides equal.

Choices:

A. If a polygon has all its sides equal, then it is regular.
B. A polygon is regular, if it has all its sides equal.
C. If a polygon is regular, then it has all its sides equal.
D. A regular polygon has all its sides equal.
Correct Answer: C

Solution:

Step 1: Among the statements listed, the if-then statement in choice C is correct.

Quick Summary

If-then statements are fundamental in deductive reasoning.
The 'If' part is the hypothesis (antecedent), and the 'then' part is the conclusion (consequent).
If the hypothesis is true and the conclusion is false, the if-then statement is false. Otherwise, it is true.

\[ A \implies B \]

🍎 Teacher Insights

Use real-world examples to illustrate if-then statements. Emphasize the difference between an if-then statement and its converse. Use truth tables to explain the logical validity of if-then statements.

🎓 Prerequisites

Basic Algebra
Understanding of variables
Deductive Reasoning

Check Your Knowledge

Q1: Identify the hypothesis in the statement: If it rains, then the ground is wet.

The ground is wet. It rains. The ground is not wet. It does not rain.

Q2: Which of the following is the converse of: If a shape is a square, then it has four sides?

If a shape has four sides, then it is a square. If a shape is not a square, then it does not have four sides. If a shape does not have four sides, then it is not a square. A shape is a square if and only if it has four sides.

Frequently Asked Questions

Q: What is the converse of an if-then statement?
A: The converse of 'If A, then B' is 'If B, then A.'

Q: When is an if-then statement considered false?
A: An if-then statement is false only when the hypothesis (A) is true, and the conclusion (B) is false.