3. Logic

Determine the truth value of the following statement and find its negation.

Not all puppies are corgis.

Let $p$: Some people like cats. $q$: All cats have fur. Represent the following statement symbolically and determine its truth value.

At least one cat does not have fur.

Determine the truth value of the following statement and find its negation.

All squares are rectangles.

Let $p$: Some people like cats. $q$: All cats have fur. Represent the following statement symbolically and determine its truth value.

No people like cats.

Determine the truth value of the following statement and find its negation.

No prime number is even.

Determine the truth value of the following statement and find its negation.

Some circles are polygons.