College

Analyze the biconditional statement below and complete the instructions that follow.

A polygon is a pentagon if and only if it has five sides.

Express the given biconditional as the conjunction of two conditionals.

A. If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.
B. If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon.
C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.
D. If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon.

Answer :

Answer:

D. If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon

Step-by-step explanation:

Given statements;

A polygon is a pentagon if and only if it has five sides.

  • From the statement we see that a pentagon has 5 sides.
  • A body of this structure with 5 sides can be classified as a polygon.

Therefore, this bi-conditional statement is premised on two "if"s,

If it is a pentagon then we are dealing with a body with 5 sides.

And if such body has five sides, it is a polygon called pentagon

The correct option is D

Choice A, B and C are logically flawed.

A. If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.

The emboldened part we do not know.

B. If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon

The emboldened part is flawed.

C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.

We do not know if all pentagons have 5 sides.

Final answer:

The conjunction of two conditional statement for the biconditional 'A polygon is a pentagon if and only if it has five sides' is 'If it is a pentagon, then it has five sides' and 'If a polygon has five sides, then it is a pentagon'.

Explanation:

The given biconditional statement 'A polygon is a pentagon if and only if it has five sides' can be split into two conditional statements as follows: 'If it is a pentagon, then it has five sides' and 'If a polygon has five sides, then it is a pentagon'.

These two separate conditional statements show both possible directions of the biconditional statement. Option D correctly represents these two conditions as the conjunction of two conditional statements.

Learn more about Biconditional Statements here:

https://brainly.com/question/35695050

#SPJ2