8th grade Q2

If-then statements are one of the most important types of logical statement in mathematics. They detail a relationship between a hypothesis and a conclusion.

Definition
An if-then statement is written as "If $p$, then $q$," where:

• $p$ is the hypothesis (the condition or assumption).
• $q$ is the conclusion (the result or outcome).

This is sometimes written as

Structure
The hypothesis sets up the condition for the conclusion. The statement assumes that if the hypothesis is true, then the conclusion will also be true.

Consider:

• If $p$: "It is raining,"
• Then $q$: "The ground is wet."

The if-then statement is: "If it is raining, then the ground is wet."

Examples

1: "If you study, then you will pass the test."

• Hypothesis: "You study."
• Conclusion: "You will pass the test."

2: "If a number is even, then it is divisible by 2."

• Hypothesis: "A number is even."
• Conclusion: "It is divisible by 2."

Important Notes:

• The hypothesis does not guarantee the truth of the conclusion in all cases unless the statement is valid.
• The statement only claims that the conclusion follows from the hypothesis when the hypothesis is true.

High level mathematics is all about demonstrating the truthfulness of if-then statements.