Question

write a true conditional and write a true converse that has a false converse.
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 and set c, then set a is in set c.

Explanation:

A conditional statement has the form "if p, then q". The converse of a conditional statement "if p, then q" is "if q, then p". For the statement "If a polygon is a pentagon, then it is a closed - figure with exactly five sides", the converse "If a closed - figure has exactly five sides, then it is a pentagon" is true. In option B, the converse "If there are clouds in the sky, then it is raining" is false as clouds don't always mean rain. In option C, the converse "If it is a school day, then it is Monday" is false as school days can be other weekdays too. In option D, the converse of set - related statement has logical flaws in set - theory concepts.

Answer:

A. If a closed figure has exactly five sides, then it is a pentagon.