Question

PLEASE HELP QUICK

If a polygon is a quadrilateral, then it is a square.


1. Identify the hypothesis of the conditional statement.




2. Identify the conclusion of the conditional statement.





3. Is the conditional statement true? If it is false, provide a counterexample.





4. What is the inverse of the conditional statement.





5. What is the converse of the conditional statement.





6. Write the biconditional statement. If a biconditional statement cannot be written, explain why it can’t be. (1 point)

Answer 1

A conditional statement is something like:

If P, then Q.

P = hypothesis.

Q = conclusion.

In this case, we have:

"If a polygon is a quadrilateral, then it is a square".

1) The hypothesis is: a polygon is a quadrilateral

2) The conclusion is: it is a square

3) It is not true, because there are other quadrilaterals that are not squares, for example, the rectangles.

4) The inverse of a conditional statement is (using the same notation than above)

If not P, then not Q.

In this case is:

"If a polygon is not a quadrilateral, then it is not a square"

(this is true)

5) A converse statement is:

If Q, then P

In this case is:

"if it is a square, then the polygon is a quadrilateral"

(Also true)

6) A biconditional statement is written as:

P if and only if Q.

In this case is:

A polygon is a quadrilateral if and only if it is a square.

(This is false)