Question

1. the biconditional form of the statement would be:

• if a figure has four equal sides, then it is a square.
• a figure is a square if and only if it has four equal sides
• if a figure is not a square, then it does not have four equal sides.
• if a figure does not have four equal sides, then it is not a square.

1. the inverse form of the statement would be:

• if a figure is not a square, then it does not have four equal sides.
• a figure is a square if and only if it has four equal sides
• if a figure does not have four equal sides, then it is not a square.
• if a figure has four equal sides, then it is a square.

Explanation:

Question 2

A biconditional statement is of the form "P if and only if Q", which means both "if P then Q" and "if Q then P" are true. The original statement (implicit) is likely "If a figure is a square, then it has four equal sides" and its converse "If a figure has four equal sides, then it is a square". The biconditional combines these as "A figure is a square if and only if it has four equal sides". The other options are a conditional (first), contrapositive (third), or inverse (fourth) or just a conditional, not biconditional.

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q". Assuming the original statement is "If a figure is a square, then it has four equal sides" (where P: figure is a square, Q: figure has four equal sides), the inverse is "If a figure is not a square, then it does not have four equal sides". The second option is biconditional, third is contrapositive, fourth is original conditional.

Answer:

B. A figure is a square if and only if it has four equal sides

Question 3