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 $x \in A$ and $A \not\subset B$, then $x \in B$
Let $A=\{1,2,\{3,4\}, 5\} .$ Which of the following statements are incorrect and why ?
$\{1,2,5\}\subset A$
The set $A = \{ x:x \in R,\,{x^2} = 16$ and $2x = 6\} $ equals
If a set $A$ has $n$ elements, then the total number of subsets of $A$ is
The number of proper subsets of the set $\{1, 2, 3\}$ is