The set $A = \{ x : x \in \mathbb{R}, x^2 = 16 \text{ and } 2x = 6 \}$ is equal to

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $A \not\subset B$ and $B \not\subset C$,then $A \not\subset C$.

Let $A, B,$ and $C$ be sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$. Show that $B = C$.

Examine whether the following statement is true or false:
$\{a\} \in \{a, b, c\}$

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$,then the value of $m \times n$ is

Make correct statements by filling in the symbols $\subset$ or $\not\subset$ in the blank spaces:
${ x:x \text{ is a triangle in a plane} } \dots { x:x \text{ is a rectangle in the plane} }$