Note that if an animal is a member of the set \(\lnot A,\) then it cannot be a duckling, and it cannot be a platypus.

Next. conside the set of all animals that are not mammals. This is the set:

"not **B**"

\[ = \lnot B.\]

A member of the set \(\lnot B\) cannot be a rabbit, and it cannot be a platypus.

The negation of the set "**A** or **B**" is the set

"not ( **A** or **B**)"

\[ = \lnot \left ( A \cup B \right).\]

It is the set of animals that are not either duck-billed or mammals:

It is illustrated below:

A member of the set \(\lnot \left( A \cap B\right) \) cannot be a duckling or a rabbit or a platypus.

Finally, the set animals that are not both duck-billed and mammals is the set:

"not ( A and B)"

\[ = \lnot \left( A \cap B \right).\]

It is the set of all animals that are not platypuses.