Question

reasoning
conditional statements and negations
complete the following.
(a) consider the following statement.
i am in geometry class.
check all the statements below that are negations of this statement.
□ i am in physics class.
□ it is not the case that i am in geometry class.
□ i am not in geometry class.
(b) consider the following conditional statement.
if the dress is brown, then susan likes the dress.
what is the hypothesis of this statement?
○ the dress is not red.
○ it is not true that susan owns a dress.
○ susan likes the dress.
○ susan loves the dress.
○ the dress is brown.

Explanation:

Part (a)

Step 1: Understand the original statement

The original statement is "I am in geometry class." A negation of a statement \( p \) is \(
eg p \), which means the opposite of \( p \).

Step 2: Analyze each option

• Option 1: "I am in physics class." This is not the negation of "I am in geometry class" (it's a different class, not the opposite of being in geometry).
• Option 2: "It is not the case that I am in geometry class." This is the correct negation, as it directly says the original statement is false.
• Option 3: "I am not in geometry class." This is also a correct negation, as it is the direct opposite of "I am in geometry class."

So we check the boxes for "It is not the case that I am in geometry class" and "I am not in geometry class."

Step 1: Recall the structure of a conditional statement

A conditional statement is in the form "If \( p \), then \( q \)", where \( p \) is the hypothesis (the part after "If") and \( q \) is the conclusion (the part after "then").

Step 2: Identify the hypothesis

The conditional statement is "If the dress is brown, then Susan likes the dress." The part after "If" is "the dress is brown."

Looking at the options:

• "The dress is not red" – not related to the hypothesis.
• "It is not true that Susan owns a dress" – not related.
• "Susan likes the dress" – this is the conclusion.
• "Susan loves the dress" – not related.
• "The dress is brown" – this matches the hypothesis (the part after "If").

Answer:

Check the boxes for:

• It is not the case that I am in geometry class.
• I am not in geometry class.

Part (b)