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. 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. what is the negation of the conclusion? 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 does not have exactly 5 diagonals. d. if a polygon has exactly 5 diagonals, then the polygon is not a pentagon. e. a polygon has exactly 5 diagonals. f. a polygon is not a pentagon. g. a polygon is a pentagon. h. if a polygon is a pentagon, then the polygon has exactly 5 diagonals.

Explanation:

In a conditional statement "If p, then q", p is the hypothesis and q is the conclusion. The negation of a statement is its opposite. For the hypothesis "a polygon has exactly 5 diagonals", the negation is "a polygon does not have exactly 5 diagonals". For the conclusion "the polygon is a pentagon", the negation is "a polygon is not a pentagon".

Answer:

Negation of the hypothesis: H. A polygon does not have exactly 5 diagonals.
Negation of the conclusion: F. A polygon is not a pentagon.