8th grade Q2

To transform a statement into an equivalent if-then statement, you rewrite the statement in the form “If $p$, then $q$” while preserving its original logical meaning.

Steps to Transform a Statement

1. Identify the Hypothesis and Conclusion: Break the statement into two parts: the assumption $p$ (hypothesis) and the result $q$ (conclusion).
2. Rewrite in If-Then Form: Write the statement in the form "if $p$, then $q$".
3. Verify Logical Equivalence: Ensure that the transformed statement is logically consistent with the original.

Example

Original statement: "You will fail the test unless you don't study."

Identify Hypothesis and Conclusion:

• Hypothesis: "You study" ($p$).
• Conclusion: "You will pass the test" ($q$).

Rewrite in If-Then Form:

"If you study, then you will pass the test" ($p\to q$).