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

Let $A$ and $B$ be sets. If $A \cap X = B \cap X = \phi$ and $A \cup X = B \cup X$ for some set $X$,show that $A = B$. (Hint: Use $A = A \cap (A \cup X)$,$B = B \cap (B \cup X)$ and the Distributive law.)

Let $A = \{1, 2, 3, \ldots, 10\}$ and $B = \left\{\frac{m}{n} : m, n \in A, m < n \text{ and } \gcd(m, n) = 1\right\}$. Then $n(B)$ is equal to:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $B$ or $C$.

The set $A = \{ x : x \ne x \}$ represents:

List all the elements of the following set:
$A = \{ x:x \text{ is an odd natural number} \}$