If $A=$ set of letters in the word RAJASTHAN and $B=$ set of letters in the word AMRITSAR.
Verify the following results.

$n\left(A-B\right)=n\left(A\right)-n\left(A\cap B\right)=n\left(A\cup B\right)-n\left(B\right)$

(i) The value of $x$

(ii) $n\left(A\cup B\right)$

(i) $Y\subset X\cup Y$

(ii) $X\cap Y\subset X$

(iii) $X\subset Y\Rightarrow X\cap Y=X$

(i) All the students who like mango also like apple, but some students who like apple, do not like mango.

(ii) There is no student who like both mango and apple

(iii) Some of the students like mango but do not like apple, some like apple but do not like mango, and some like both.

(iv) Not all students like mango but every students liking apple also likes mango.