Question

consider the given statement.
not every shoe on display is new.
for each statement below, determine whether it is a negation of the given statement.

no shoe on display is new.
at least one shoe on display is new.
some shoes on display are not new.
every shoe on display is new.

Explanation:

1. The original statement "Not every shoe on display is new" is logically equivalent to "Some shoes on display are not new".
2. The negation of a statement reverses its truth value. The negation of "Not every shoe is new" is the universal positive claim "Every shoe on display is new".
3. The other statements either match the original claim or do not directly reverse its logical meaning, so they are not negations.

Answer:

No shoe on display is new. → No
At least one shoe on display is new. → No
Some shoes on display are not new. → No
Every shoe on display is new. → Yes