8th grade Q2

The converse of an if-then statement is formed by switching the hypothesis and the conclusion.

If the original statement is

"If $p$, then $q$" ($p\to q$),

the converse is

"If $q$, then $p$" ($q\to p$).

Steps to Determine the Converse:

1. Start with the original Statement:
   Write the statement in the form "If $p$, then $q$."
2. Switch the hypothesis and conclusion:
   Rewrite the statement as "If $q$, then $p$.

Note: Just because the original statement is true, does not mean the converse is true.

Example

Original statement: "If it rains, then the ground will be wet."

• Hypothesis: "It rains" ($p$).
• Conclusion: "The ground will be wet" ($q$).

Converse: "If the ground is wet, then it rained."

• Hypothesis: "The ground is wet" ($q$).
• Conclusion: "It rained" ($p$).

Here you can see why the converse isn't always true. The ground could be wet for reasons other than rain, such as watering the garden.

Key Points:

• The converse switches the roles of the hypothesis and conclusion.
• The converse is not logically equivalent to the original statement.