The provided image presents a logical statement followed by a set of other statements, asking to determine if each one is a negation of the given statement:

The original statement is:

• "Some gifts in the bag are not wrapped."

Let's analyze each option to see whether it is a negation:

1. All gifts in the bag are wrapped.

   • This is not a direct negation. The negation of "some are not wrapped" would be closer to "none are wrapped."
   • Answer: No

2. None of the gifts in the bag are wrapped.

   • This is a possible negation because it directly contradicts "some are not wrapped" by implying that all are unwrapped.
   • Answer: Yes

3. At least one gift in the bag is wrapped.

   • This does not contradict the original statement. In fact, the original statement allows for the possibility that some gifts may be wrapped.
   • Answer: No

4. Some gifts in the bag are wrapped.

   • This is consistent with the original statement, which does not imply that all gifts are unwrapped. Therefore, it is not a negation.
   • Answer: No

Would you like further details on these answers?

Related questions:

1. What is the formal rule for negating "some" statements in logic?
2. How would you negate a statement like "all gifts are wrapped"?
3. Can two logical statements both be true without being negations?
4. How would the truth value of the original statement change if the word "some" were replaced with "all"?
5. What is the difference between a contradiction and a negation in logic?

Tip: When negating a statement involving "some" or "all," the opposite must cover the full spectrum. For example, the negation of "some" is "none."