State which of the following sets are finite or infinite: $\{ x:x \in N \text{ and } 2x - 1 = 0 \}$

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 $x \notin B,$ then $x \notin A$.

Let $A, B, C$ be subsets of a set $X$. Which of the following set-theoretic statements is valid?

Which of the following pairs of sets are disjoint?
$A = \{ x : x \text{ is an even integer} \}$
$B = \{ x : x \text{ is an odd integer} \}$

State whether the following statement is true or false. Justify your answer.
${2, 6, 10}$ and ${3, 7, 11}$ are disjoint sets.

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