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 $A$ and $B$ are sets, then $A \cap (B -A)$ is

Consider the following relations :

$(1) \,\,\,A – B = A – (A \cap B)$

$(2) \,\,\,A = (A \cap B) \cup (A – B)$

$(3) \,\,\,A – (B \cup C) = (A – B) \cup (A – C)$

which of these is/are correct

If $A$ and $B$ are two sets such that $A \subset B$, then what is $A \cup B ?$

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\} $