Question

write the negation of the hypothesis and the negation of the conclusion for the conditional. if a polygon has exactly 5 diagonals, then the polygon is a pentagon. what is the negation of the hypothesis? a. if a polygon does not have exactly 5 diagonals, then the polygon is not a pentagon. b. if a polygon does not have exactly 5 diagonals, then the polygon is a pentagon. c. a polygon is not a pentagon. d. a polygon has exactly 5 diagonals. e. if a polygon is a pentagon, then the polygon has exactly 5 diagonals. f. if a polygon has exactly 5 diagonals, then the polygon is not a pentagon. g. a polygon is a pentagon. h. a polygon does not have exactly 5 diagonals.

Explanation:

In a conditional statement "If p, then q", p is the hypothesis. Here, the hypothesis is "a polygon has exactly 5 diagonals". The negation of a statement simply means the opposite. So the negation of the hypothesis is that the polygon does not have exactly 5 diagonals.

Answer:

H. A polygon does not have exactly 5 diagonals.