Let $A=\{1,2,3,4,5,6,7,8,9,10\}$ and $B=\{2,3,5,7\} .$ Find $A \cap B$ and hence show that $A \cap B = B$

If $aN = \{ ax:x \in N\} $ and $bN \cap cN = dN$, where $b$, $c \in N$ are relatively prime, then

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 $V =\{a, e, i, o, u\}$ and $B =\{a, i, k, u\} .$ Find $V - B$ and $B - V$

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 $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find $B \cap C$