Question

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

statement: jonah either plays soccer or is on the swim team.

• jonah does not play soccer, but he is on the swim team.
• jonah does not play soccer and is not on the swim team.
• if jonah plays soccer, he is also on the swim team.
• jonah plays soccer and is on the swim team.

Explanation:

The original statement is a logical "or" statement: \( P \lor Q \), where \( P \) is "Jonah plays soccer" and \( Q \) is "Jonah is on the swim team". The negation of \( P \lor Q \) is \(
eg P \land
eg Q \) (by De Morgan's laws), which means Jonah does not play soccer AND Jonah is not on the swim team. Now we analyze each option:

• First option: \(

eg P \land Q \), which is not the negation.

• Second option: \(

eg P \land
eg Q \), this matches the negation of \( P \lor Q \).

• Third option: This is an implication (\( P \to Q \)), not a negation.
• Fourth option: \( P \land Q \), which is not the negation.

Answer:

B. Jonah does not play soccer and is not on the swim team. (Note: Here we assume the second option is labeled as B; if the original options had labels like A, B, C, D, we use the correct label. Since the user's options are circles, we identify the correct one as the second option which is "Jonah does not play soccer and is not on the swim team".)