Question

there are several statements in the table below.
for each, determine whether it is a negation of this statement.
i am drawing a circle.
i am not drawing a rectangle.
it is not the case that i am drawing a circle.
i am not drawing a circle.
i am drawing a triangle.

Explanation:

Step1: Analyze the first statement

The original statement is about drawing a circle. The first option "I am not drawing a rectangle" is about a rectangle, not related to negating the circle - drawing statement.

Step2: Analyze the second statement

The second option "It is not the case that I am drawing a circle" is a direct logical negation. If \(p\) is "I am drawing a circle", then \(
eg p\) (not \(p\)) is "It is not the case that \(p\)".

Step3: Analyze the third statement

The third option "I am not drawing a circle" is also a direct negation. If the original positive statement is \(p\), then \(
eg p\) can be written in this simple "not - verb" form.

Step4: Analyze the fourth statement

The fourth option "I am drawing a triangle" is about a triangle. It does not address the negation of drawing a circle. It just gives an alternative shape, not a logical negation.

Answer:

• "I am not drawing a rectangle": No
• "It is not the case that I am drawing a circle": Yes
• "I am not drawing a circle": Yes
• "I am drawing a triangle": No