Sets Test - 14...

Let $$P =$$ Set of all integral multiples of $$3 $$; $$Q =$$ Set of integral multiples of $$4 $$; $$R =$$ Set of all integral multiples of $$6$$. Consider the following relations :
$$1 $$ $$\displaystyle P\cup Q=R$$
$$2.$$ $$\displaystyle P\subset R$$
$$3.$$ $$\displaystyle R\subset \left ( P\cup Q \right )$$
Which of the relations given above is/are correct ?

In a locality two-thirds of the people have cable TV one-fifth have Dish TV and one-tenth have both What is the fraction of people having either cable TV or Dish TV?

In an examination $$70\%$$ students passed both in Mathematics and Physics $$85\%$$ passed in Mathematics and $$80\%$$ passed in Physics If $$30$$ students have failed in both the subjects then the total number of students who appeared in the examination is equal to : 

In a class of $$50$$ students $$35$$ opted for Mathematics and $$37$$ opted for Biology How may have opted for only Mathematics? ( Assume that each student has to opt for at least one of the subjects)

If $$n(A) = 65, n(B) = 32$$ and $$\displaystyle n\left ( A\cap B \right )=14 $$, then $$\displaystyle n\left ( A\Delta  B \right ) $$ equals

If $$n(A) = 115$$, $$n(B) = 326$$, $$n(A - B) = 47$$ then $$\displaystyle n\left ( A\cup B \right )$$ is equal to

If $$X$$ and $$Y$$ are any two non empty sets then what is $$\displaystyle \left ( X-Y \right )'$$ equal to?

If $$A$$ and $$B$$ are non empty sets and A' and B' represents their compliments respectively then

If $$\displaystyle \xi =\left \{ 2,3,4,5,6,7,8,9,10,11 \right \}$$
$$\displaystyle A =\left \{ 3,5,7,9,11 \right \}$$
$$\displaystyle B =\left \{ 7,8,9,10,11 \right \}$$, then find $$(A - B)'$$

If $$\displaystyle Q=\left\{ x:x=\frac { 1 }{ y } ,where\  \ y\ \in \ N \right\} $$, then find the correct one.