Write the following set in the set-builder form: $\{ 2, 4, 6, \dots \}$

Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$ and $C = \{0, 2, 4, 6, 8\}$,which of the following may be considered as a universal set for all the three sets $A$,$B$ and $C$?

The dual of $(x+y) \cdot (x^{\prime} \cdot 1)$ is:

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:

For any sets $A$ and $B$,show that $P(A \cap B) = P(A) \cap P(B).$

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give an example.
If $A \subset B$ and $B \subset C$,then $A \subset C$.