Question

1. which of the following answer choices shows the negation of the statement below?

statement: if liz is in eighth grade, then she takes spanish.
liz is in eighth grade, and she does take spanish.
liz is not in eighth grade, but she does take spanish.
liz is in eighth grade, and she does not take spanish.
liz is not in eighth grade, and she does not take spanish.

Explanation:

Step1: Recall the negation of a conditional statement

The statement is of the form "If \( p \), then \( q \)" where \( p \) is "Liz is in eighth grade" and \( q \) is "she takes Spanish". The negation of "If \( p \), then \( q \)" is \( p \land
eg q \) (read as \( p \) and not \( q \)).

Step2: Analyze each option

• Option 1: \( p \land q \) (Liz is in eighth grade and she takes Spanish) – this is not the negation.
• Option 2: \(

eg p \land q \) (Liz is not in eighth grade and she takes Spanish) – this is not the negation.

• Option 3: \( p \land

eg q \) (Liz is in eighth grade and she does not take Spanish) – this matches the negation of the conditional statement.

• Option 4: \(

eg p \land
eg q \) (Liz is not in eighth grade and she does not take Spanish) – this is not the negation.

Answer:

Liz is in eighth grade, and she does not take Spanish. (The third option)