State whether the following set is finite or infinite:
The set of circles passing through the origin $(0,0)$.

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 $B \subset C$,then $A \subset C$.

If $y = 3[x] + 1 = 4[x - 1] - 10$,then $[x + 2y]$ is equal to (where $[.]$ is the $Greatest$ $Integer$ $Function$)

Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$0 \dots A$

Which of the following is an empty set?

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
${1, 2, 5} \subset A$