Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey, $80$ played cricket and basketball and $40$ played cricket and hockey; $24$ played all the three games. The number of boys, who did not play any game is

If two sets $A$ and $B$ having $3$ and $6$ elements respectively, then which of the following is/are correct?

I. The minimum number of elements of $\left(A\cup B\right)=6$.
II. The maximum number of elements of $\left(A\cap B\right)=3$.

Select the correct answer using the code given below

If $A$ is any set and $P\left(A\right)$ is its power set, then which of the following is/are correct?

I. $P\left(A\right)\cap P\left(B\right)=P(A\cap B)$
II. $P\left(A\right)\cup P\left(B\right)=P(A\cup B)$

Select the correct answer using the code given below

A relation between three sets is established using two expressions, $(A\cup B)=(A\cup C)$ and $(A\cap B)=(A\cap C)$, which stays valid if and only if

I. $B=C$

II. $A=B=C$

III. $A=C$

Which of the above statement(s) is / are correct?

Let $U=\left\{x\in N: 1\le x\le 10\right\}$ be the universal set, $N$ being the set of natural numbers.

If $A=\left\{1,2,3,4\right\}$ and $B=\left\{2,3,6,10\right\}$, then what is the complement of $(A-B)$? 

If $A=\left\{x\in R: x^2+6x-7<0\right\}$ and $B=\left\{x\in R: x^2+9x+14>0\right\}$, then which of the following is/are correct?

$\mathrm{I}.$$\left(A\cap B\right)=\left(-2,1\right)$                $\mathrm{II}.$ $\left(A\backslash B\right)=\left(-7,-2\right)$

Select the correct answer using the code given below 

$A, B, C$ and $D$ are four sets such that $A\cap B=C\cap D=\mathrm{\varphi }$. Consider the following

$\mathrm{I}.$ $A\cup C$ and $B\cup D$ are always disjoint

$\mathrm{II}.$ $A\cap C$ and $B\cap D$ are always disjoint

Which of the above statement(s) is / are correct?