1. The problem asks to express the proposition \(\neg p\) in English. 2. Given \(p\): "I bought a lottery ticket this week." 3. The negation \(\neg p\) means "not p", so it is the opposite of \(p\). 4. Therefore, \(\neg p\) can be expressed as: "I did not buy a lottery ticket this week." This is the English sentence representing the negation of \(p\).