Question

For two sets $A\cup B=A$ iff
(a) $B\subseteq A$
(b) $A\subseteq B$
(c) $A\ne B$
(d) $A=B$

Answer 1

(a) $B\subseteq A$
The union of two sets is a set of all those elements that belong to A or to B or to both A and B.
If A$\cup$B = A, then B$\subseteq$A.