Question

write the negation of the hypothesis and the negation of the conclusion for the conditional. if a polygon has exactly 14 diagonals, then the polygon is a heptagon. what is the negation of the conclusion? a. if a polygon is a heptagon, then the polygon has exactly 14 diagonals. b. a polygon has exactly 14 diagonals. c. a polygon is not a heptagon. d. if a polygon has exactly 14 diagonals, then the polygon is not a heptagon. e. if a polygon does not have exactly 14 diagonals, then the polygon is a heptagon. f. a polygon does not have exactly 14 diagonals. g. a polygon is a heptagon. h. if a polygon does not have exactly 14 diagonals, then the polygon is not a heptagon.

Explanation:

In a conditional statement "If p, then q", the conclusion is q. The negation of a statement simply means the opposite. Here, the conclusion is "the polygon is a heptagon", so its negation is "a polygon is not a heptagon".

Answer:

C. A polygon is not a heptagon