Determine whether the following set is finite or infinite:
The set of positive integers greater than $100$.

Prove that for any sets $A$ and $B$,$A \cap (A \cup B) = A$.

If $aN = \{ax : x \in N\}$ and $bN \cap cN = dN$,where $b, c \in N$ are coprime numbers,then:

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is an even natural number} } \dots { x:x \text{ is an integer} }$

Consider the sets $\phi, A = \{1, 3\}, B = \{1, 5, 9\}, C = \{1, 3, 5, 7, 9\}$. Insert the symbol $\subset$ or $\not\subset$ between the following pair of sets: $\phi \dots B$.

If $A = \{1, 2, 3, \ldots, 10\}$,then the number of non-empty subsets of $A$ containing only odd numbers is