Question

write a true conditional that has a true converse. choose the correct answer below. a. if a polygon is a pentagon, then it is a closed figure with exactly five sides. b. if it is raining, then there are clouds in the sky. c. if it is monday, then it is a school day. d. if set a and set b are in set c, then set a is in set c.

Explanation:

Step1: Recall conditional and converse statements

A conditional statement is of the form "if p, then q" and its converse is "if q, then p".

Step2: Analyze Option A

The conditional "If a polygon is a pentagon, then it is a closed - figure with exactly five sides" is true. Its converse "If a figure is a closed - figure with exactly five sides, then it is a pentagon" is also true.

Step3: Analyze Option B

The conditional "If it is raining, then there are clouds in the sky" is true. Its converse "If there are clouds in the sky, then it is raining" is false as there can be clouds without rain.

Step4: Analyze Option C

The conditional "If it is Monday, then it is a school day" may be false (e.g., on holidays) and its converse analysis is not relevant as the original conditional is not always true.

Step5: Analyze Option D

The statement about set - membership is a set - theory related conditional, but it's a different type of logical statement from the typical "if - then" statements about common facts.

Answer:

B. If it is raining, then there are clouds in the sky.