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 $B \subset C,$ then $A \subset C$
State whether each of the following set is finite or infinite :
The set of lines which are parallel to the $x\,-$ axis
Let $S=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to
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 $\} $
What universal set $(s)$ would you propose for each of the following :
The set of right triangles