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:
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