Question

consider the given statement.
every pot in the kitchen has a lid.
for each statement below, determine whether it is a negation of the given statement.

not every pot in the kitchen has a lid.
some pots in the kitchen have a lid.
no pot in the kitchen has a lid.
at least one pot in the kitchen does not have a lid.

Explanation:

The original statement is a universal affirmative claim: "All pots have lids." The logical negation of a universal statement "All A are B" is "There exists at least one A that is not B".

• "Not every pot has a lid" directly contradicts the universal claim, so it is a negation.
• "Some pots have a lid" is a weaker affirmative statement that does not contradict the original claim, so it is not a negation.
• "No pot has a lid" is an extreme opposite, not the logical negation (it is a universal negative, not the denial of the original universal affirmative).
• "At least one pot does not have a lid" matches the standard logical negation of the original universal statement.

Answer:

1. Not every pot in the kitchen has a lid. → Yes
2. Some pots in the kitchen have a lid. → No
3. No pot in the kitchen has a lid. → No
4. At least one pot in the kitchen does not have a lid. → Yes