Question

determine the validity of the conditional statement below and the validity of its converse. if possible, re-write the given statement as a biconditional.
if a polygon is a quadrilateral, then it has four sides.
show your work here.
conditional statement is:
true false
converse of statement is:
true false
biconditional form:
a polygon is a quadrilateral if and only if it has four sides.
if a polygon has four sides, then it is a quadrilateral.
a polygon is a quadrilateral if and only if it does not have four sides.
biconditional is not possible.

Explanation:

Step1: Analyze the conditional statement

A quadrilateral is defined as a polygon with four sides. So the statement "If a polygon is a quadrilateral, then it has four sides" is true because by definition, quadrilaterals have four sides.

Step2: Find the converse of the statement

The converse of "If \( p \), then \( q \)" is "If \( q \), then \( p \)". So the converse of "If a polygon is a quadrilateral, then it has four sides" is "If a polygon has four sides, then it is a quadrilateral". A polygon with four sides is, by definition, a quadrilateral, so the converse is also true.

Step3: Determine the biconditional form

A biconditional statement is " \( p \) if and only if \( q \)" when both the conditional (\( p \to q \)) and its converse (\( q \to p \)) are true. Since both the original statement and its converse are true, the biconditional form is "A polygon is a quadrilateral if and only if it has four sides".

Answer:

s:
Conditional statement is: True
Converse of statement is: True
Biconditional form: A polygon is a quadrilateral if and only if it has four sides.