Question

there are several statements in the table below. for each, determine whether it is a negation of this statement.
i am drawing a triangle.
|statement|negation?

i am not drawing a rectangle.	yes ○	no ○
it is not the case that i am drawing a rectangle.	yes ○	no ○
it is not the case that i am drawing a triangle.	yes ○	no ○
i am drawing a rectangle.	yes ○	no ○

Explanation:

Step1: Understand Negation

A negation of a statement \( P \) is a statement that is true when \( P \) is false and false when \( P \) is true. The original statement is \( P \): "I am drawing a triangle." Its negation should be "It is not the case that I am drawing a triangle" (which is \(
eg P \)).

Step2: Analyze Each Statement

• "I am not drawing a rectangle": This is about a rectangle, not the triangle. So it's not a negation of \( P \).
• "It is not the case that I am drawing a rectangle": Again, about a rectangle, not the triangle. Not a negation of \( P \).
• "It is not the case that I am drawing a triangle": This is \(

eg P \), so it is the negation.

• "I am drawing a rectangle": About a rectangle, not the triangle. Not a negation of \( P \).

Answer:

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

(To mark in the table: For each row, circle "Yes" or "No" as above. The only one with "Yes" is "It is not the case that I am drawing a triangle".)