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 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.
jonah does not play soccer, but he 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 is not on the swim team. The other options do not represent the negation: the second is a conditional, the third is \( P \land Q \), and the fourth is \(
eg P \land Q \), none of which negate \( P \lor Q \).

Answer:

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