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

If $A, B$ and $C$ are any three sets, then $A -(B  \cup C)$  is equal to

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

$A=\{a, e, i, o, u\} B=\{a, b, c\}$

Show that for any sets $\mathrm{A}$ and $\mathrm{B}$, $A=(A \cap B) \cup(A-B)$ and $A \cup(B-A)=(A \cup B).$

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

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

Let $P=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then