Make correct statements by filling in the symbols $\subset$ or $ \not\subset $ in the blank spaces:
$\{ x:x$ is an equilateral triangle in a plane $\} \ldots \{ x:x$ is a triangle in the same plane $\} $
$\{ x:x$ is an equilateral triangle in a plane $\} \subset \{ x:x$ is a triangle in the same plane $\} $
List all the elements of the following sers :
$E = \{ x:x$ is a month of a year not having $ 31 $ days ${\rm{ }}\} $
Write down all the subsets of the following sets
$\{ a\} $
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 $x \notin A$
Decide, among the following sets, which sets are subsets of one and another:
$A = \{ x:x \in R$ and $x$ satisfy ${x^2} - 8x + 12 = 0 \} ,$
$B=\{2,4,6\}, C=\{2,4,6,8 \ldots\}, D=\{6\}$
Write the following sets in the set-builder form :
${\rm{\{ 2,4,8,16,32\} }}$