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13. [-14 Points] DETAILS AUFEXCE3 3.4.015. Consider the following statement. Every parallelogram is a quadrilateral. (a) Write the converse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. O If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. O If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (b) Write the inverse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (c) Write the contrapositive of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram.

Answer 1

13.) a.) A converse of a given statement involves the interchanging of hypothesis and the conclusion .In the given statement "Every parallelogram is a quadrilateral " , we will interchange the hypothesis with the conclusion and the converse will be -''If a figure is a quadrilateral then it is a parallelogram ''.

Hence, option (4.) is correct .

b.)To write the inverse of a given statement ,we are supposed to take negation of both hypothesis and the conclusion .So the inverse of the given statement will be - ''If a figure is not a parallelogram then it is not a quadrilateral ''.

Hence option (5.) is correct .

c.) To write the contrapositive of a statement we interchange the hypothesis with the conclusion in the inverse statement . So the contrapositive of the given statement will be -''If a figure is not a quadrilateral then it is not a parallelogram''.

Hence ,option (6.) is correct .