If $A$ and $B$ are any two sets, then $A \cup (A \cap B) $ is equal to
$A$
$B$
${A^c}$
${B^c}$
If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {e^x},\,x \in R\} $; $B = \{ (x,\,y):y = x,\,x \in R\} ,$ then
Let $A$ and $B$ be subsets of a set $X$. Then
Show that the following four conditions are equivalent:
$(i)A \subset B\,\,\,({\rm{ ii }})A - B = \phi \quad (iii)A \cup B = B\quad (iv)A \cap B = A$
If $A, B, C$ be three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$, then
If $A=\{3,6,9,12,15,18,21\}, B=\{4,8,12,16,20\},$ $C=\{2,4,6,8,10,12,14,16\}, D=\{5,10,15,20\} ;$ find
$D-B$