If $A$ and $B$ are any two sets, then $A \cap (A \cup B)$ is equal to

Find the union of each of the following pairs of sets :

$A=\{1,2,3\}, B=\varnothing$

Using that for any sets $\mathrm{A}$ and $\mathrm{B},$

$A \cup(A \cap B)=A$

Let $A :\{1,2,3,4,5,6,7\}$. Define $B =\{ T \subseteq A$ : either $1 \notin T$ or $2 \in T \}$ and $C = \{ T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is $\dots\dots$

Which of the following pairs of sets are disjoint 

$\{a, e, i, o, u\}$ and $\{c, d, e, f\}$

Find the union of each of the following pairs of sets :

$A = \{ x:x$ is a natural number and $1\, < \,x\, \le \,6\} $

$B = \{ x:x$ is a natural number and $6\, < \,x\, < \,10\} $