Question

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

Answer 1

Answer:

1) Hypothesis: A polygon is a quadrilateral,

2) Conclusion:  It is a square.

3) Counter example, A polygon is a square quadrilateral if  all the sides are equal.

4)  Inverse : If a polygon is not  a quadrilateral, then it is not  a square.

5)  Converse :If a square is quadrilateral then it is a polygon.

6) Biconditional statement :If a square is a  polygon quadrilateral , then the polygon has equal sides.

Step-by-step explanation:

The hypothesis of the conditional statement is the one which starts immediately after the word if and the conclusion is the one given after then.

1) Hypothesis: A polygon is a quadrilateral,

2) Conclusion:  It is a square.

3) It is false because the square is a quadrilateral which has four side equal . The given statement does not contain anything defining the quadrilateral as a square.

Counter example, A polygon is a square quadrilateral if  all the sides are equal.

4) The inverse is obtained by  finding the inverse of both the hypothesis and conclusion.

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

5) The converse is obtained by changing the hypothesis into conclusion and vice versa.

If a square is quadrilateral then it is a polygon.

6) A bi conditional statement is one  in which both the hypothesis and the conclusion can be treated as the hypothesis or the conclusion and vice versa. Meaning it can be operated both ways

Conclusion as hypothesis

Hypothesis as conclusion

If a square is a  polygon quadrilateral , then the polygon has equal sides.

Hypothesis : A square is a  polygon quadrilateral.

Conclusion : The polygon has equal sides.

Hypothesis: The  quadrilateral  polygon has equal sides.

Conclusion : The  quadrilateral polygon is a square.