Question

identify the negation of each statement. ∠hjk and ∠ity are supplementary angles. the negation of the statement is dropdown. all pentagons have five sides. the negation of the statement is dropdown. all circles have zero angles. the negation of the statement is dropdown. mindy has a blue pencil. the negation of the statement is dropdown.

Explanation:

For the statement “\(\angle HJK\) and \(\angle JTY\) are supplementary angles”

Step 1: Recall the negation of a statement

The original statement claims that two angles are supplementary. The negation will be that they are not supplementary.

Step 2: Form the negation

So the negation is “\(\angle HJK\) and \(\angle JTY\) are not supplementary angles”.

For the statement “All pentagons have five sides”

Step 1: Recall the negation of a universal statement

A universal statement “All \(A\) are \(B\)” has the negation “Some \(A\) are not \(B\)” (or “There exists an \(A\) that is not \(B\)”).

Step 2: Apply to the given statement

Here, \(A\) is pentagons and \(B\) is having five sides. So the negation is “Some pentagons do not have five sides” (or “There exists a pentagon that does not have five sides”).

For the statement “All circles have zero angles”

Step 1: Recall the negation of a universal statement

A universal statement “All \(A\) are \(B\)” has the negation “Some \(A\) are not \(B\)” (or “There exists an \(A\) that is not \(B\)”).

Step 2: Apply to the given statement

Here, \(A\) is circles and \(B\) is having zero angles. So the negation is “Some circles do not have zero angles” (or “There exists a circle that does not have zero angles”).

For the statement “Mindy has a blue pencil”

Answer:

s:

• Negation of “\(\angle HJK\) and \(\angle JTY\) are supplementary angles”: \(\boldsymbol{\angle HJK}\) and \(\boldsymbol{\angle JTY}\) are not supplementary angles.
• Negation of “All pentagons have five sides”: \(\boldsymbol{\text{Some pentagons do not have five sides}}\) (or “There exists a pentagon that does not have five sides”).
• Negation of “All circles have zero angles”: \(\boldsymbol{\text{Some circles do not have zero angles}}\) (or “There exists a circle that does not have zero angles”).
• Negation of “Mindy has a blue pencil”: \(\boldsymbol{\text{Mindy does not have a blue pencil}}\).