State the converse and the contrapositive of the given proposition If polygon AB

Question

State the converse and the contrapositive of the given proposition If polygon ABCDEF is a hexagon, then polygon ABCDEF has six sides. State the converse of the given proposition O A. Polygon ABCDEF has six sides and polygon ABCDEF is not a hexagon. O B. If polygon ABCDEF has six sides, then polygon ABCDEF is a hexagon. ° C. If polygon ABCDEF does not have six sides, then polygon ABCDEF is not a hexagon. 0 D. If polygon ABCDEF is a hexagon, then polygon ABCDEF does not have six sides. State the contrapositive of the given proposition O A. If polygon ABCDEF has six sides, then polygon ABCDEF is a hexagon. ? B. If polygon ABCDEF does not have six sides, then polygon ABCDEF is not a hexagon. O C. Polygon ABCDEF has six sides and polygon ABCDEF is not a hexagon. 0 D. If polygon ABCDEF is a hexagon, then polygon ABCDEF does not have six sides.

Explanation / Answer

If polygon ABCDEF is a hexagon, then polygon ABCDEF has six sides
Hypothesis:-Polygon ABCDEF is a hexagon
Conclusion:- Polygon ABCDEF has six sides
(1)
To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
so Converse statement will be
If polygon ABCDEF has six sides ,then polygon ABCDEF is a hexagon
( Option - B)

(2)
To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.
So statement will be
If polygon ABCDEF does not have six sides ,then polygon ABCDEF is not a hexagon
(Option B)

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