Set Theory Test...

If A and B are any two sets, then $$A\bigcup (A\bigcap B)$$ is equal to 

Let U be set with number of elements in U is 2009.
Consider the following statements : 
I if A, B are subsets of U with n $$(A \cup B)= 280 $$  then $$n(A'\cap B')=x_{1}^{3}+x_{2}^{3}=y_{1}^{3}+y_{2}^{3}$$  for some positive integers $$x_{1},x_{2},y_{1},y_{2},$$  II If A is a subset of U with n (A) = 1681 and out of these 1681 elements, exactly 1075 elements below to a subset B of U, then $$n(A-B)=m^{2}+P_{1}P_{2}P_{3}$$  for some positive integer m and distinct primes $$P_{1}P_{2}$$  Which of the statements given above is / are correct ?

The number of subjections from $$A$$ to $$B$$ is

Given $$n(U) =20, n(A) =12, n(B) =9, n(A \cap B) =4$$, where U is the universal set, A and B are subset of U, then $$n((A \cup B)^C)=$$

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

X and Y are two sets and $$f:X\rightarrow Y$$. If $$f(c)=\left\{ y;c\subset X,y\subset Y \right\} $$ and $${ f }^{ 1 }(d)=\left\{ x;d\subset Y,x\subset X \right\} $$, then the true statement is

Let N= {1, 2, 3, ........., 10}, then sum of the product of number taken two at a time from the set N is 

The set $$(A\cap B')'\cup (B\cap C)$$ is equal to?

if S is a set of p(x) is polynomial of degree <2 such that p(0)=, P(1)=1, p(x)>0 $$\forall \quad x\quad \varepsilon $$ (0, 1) then 

The solution set of $$x^{2}+5x+6=0 $$ is ........