Questions: Question 8, 3.4.29 - Section 3.4 Write the following statement in the form "if a... then b." "You can ride your bike only if the sun is shining." The statement equivalently written in the form "if a ... then b " is which of the following? A. If you can ride your bike, then the sun is shining. B. If the sun is shining, then you can ride your bike. C. If the sun is not shining, then you can ride your bike.

Question 8, 3.4.29
- Section 3.4

Write the following statement in the form "if a... then b."
"You can ride your bike only if the sun is shining."

The statement equivalently written in the form "if a ... then b " is which of the following?
A. If you can ride your bike, then the sun is shining.
B. If the sun is shining, then you can ride your bike.
C. If the sun is not shining, then you can ride your bike.

Transcript text: Question 8, 3.4.29 - Section 3.4 Write the following statement in the form "if a... then $b$." "You can ride your bike only if the sun is shining." The statement equivalently written in the form "if a ... then b " is which of the following? A. If you can ride your bike, then the sun is shining. B. If the sun is shining, then you can ride your bike. C. If the sun is not shining, then you can ride your bike.

Solution

Solution Steps

Step 1: Understand the Original Statement

The original statement is: "You can ride your bike only if the sun is shining." This implies that riding your bike is contingent upon the sun shining.

Step 2: Convert to "If a... then b" Form

The phrase "only if" indicates a necessary condition. Therefore, the statement "You can ride your bike only if the sun is shining" can be rewritten in the form "if a... then b" as: "If you can ride your bike, then the sun is shining."

Step 3: Match with the Given Options

Now, we need to match our converted statement with the given options: