In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement ?

Let $A :\{1,2,3,4,5,6,7\}$. Define $B =\{ T \subseteq A$ : either $1 \notin T$ or $2 \in T \}$ and $C = \{ T \subseteq A : T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is $\dots\dots$

If $A=\{3,5,7,9,11\}, B=\{7,9,11,13\}, C=\{11,13,15\}$ and $D=\{15,17\} ;$ find

$A \cap \left( {B \cup C} \right)$

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

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\} $