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.

• if jonah plays soccer, he is also on the swim team.
• jonah does not play soccer, but he is on the swim team.
• jonah plays soccer and is on the swim team.
• jonah does not play soccer and is not 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 neither plays soccer nor is on the swim team. Let's analyze each option:

• First option: This is a conditional (\( P \to Q \)), not a negation.
• Second option: This is \(

eg P \land Q \), not the negation of \( P \lor Q \).

• Third option: This is \( P \land Q \), not the negation.
• Fourth option: This is \(

eg P \land
eg Q \), which is the negation of \( P \lor Q \).

Answer:

Jonah does not play soccer and is not on the swim team.