Question

complete the following. (a) consider the following statement. i am drawing a rectangle. check all the statements below that are negations of this statement. it is not the case that i am drawing a rectangle. i am not drawing a triangle. i am drawing a triangle. (b) consider the following conditional statement. if mary is wearing tennis shoes, then mary has been exercising. what is the hypothesis of this statement? mary is wearing tennis shoes. mary is wearing gym shorts. mary has been exercising. mary has been sleeping. mary is not exercising now.

Explanation:

• For part (a):
• The negation of a statement \(p\) (in this case \(p=\) "I am drawing a rectangle") is a statement that is True when \(p\) is False and False when \(p\) is True.
• The statement "It is not the case that I am drawing a rectangle" is the direct logical negation of "I am drawing a rectangle".
• The statement "I am not drawing a triangle" is not related to the negation of "I am drawing a rectangle" because it is about a different geometric shape.
• The statement "I am drawing a triangle" is about drawing a different shape, not the negation of drawing a rectangle (the negation is about the absence of drawing a rectangle, not the presence of drawing another specific shape).
• For part (b):
• In a conditional statement of the form "If \(p\), then \(q\)" (\(p

ightarrow q\)), the hypothesis is \(p\).

• For the conditional statement "If Mary is wearing tennis shoes, then Mary has been exercising", the "if - part" (the hypothesis) is "Mary is wearing tennis shoes".

Answer:

• (a) \(\square\) It is not the case that I am drawing a rectangle.
• (b) Mary is wearing tennis shoes.