Let $A, B,$ and $C$ be the sets such that $A \cup B=A \cup C$ and $A \cap B=A \cap C$. Show that $B = C$

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

$\varnothing \subset A$

Let $A=\{a, e, i, o, u\}$ and $B=\{a, b, c, d\} .$ Is $A$ a subset of $B ?$ No. (Why?). Is $B$ a subset of $A ?$ No. (Why?)

In the following state whether $\mathrm{A = B}$ or not :

$A = \{ x:x$ is a multiple of $10\} ;B = \{ 10,15,20,25,30 \ldots \ldots \} $

Which set is the subset of all given sets