Set Theory Test...

The solution set of $$3 x - 4 < 8$$ over the set of non-negative square numbers is 

Let $$P$$ and $$Q$$ be two sets then what is $$\displaystyle (P\cap Q')\cup (P\cup Q)'$$ equal to ?

If $$A$$ and $$B$$ are finite sets which of the following is the correct statement?

U is a universal set and n(U) = 160. A, B and C are subset of U. If n(A) = 50, n(B) = 70, $$\displaystyle n\left ( B\cup C \right )=\Phi $$, $$\displaystyle n\left ( B\cap  C \right )=15 $$ and $$\displaystyle A\cup B\cup C=U $$. then n(C) equals

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

If A and B are two disjoint sets and N is the universal set then $$\displaystyle A^{c}\cup \left [ \left ( A\cup B \right )\cap B^{c} \right ]$$ is

Suppose $$\displaystyle A_{1},A_{2},....,A_{30}$$ are thirty sets each having 5 elements and $$\displaystyle B_{1},B_{2},....,B_{n}$$ are n sets each with 3 elements. Let $$\displaystyle \bigcup_{i=1}^{30}A_{i} = \bigcup_{j=1}^{n}B_{j}=S $$ and each elements of S belongs to exactly 10 of the $$\displaystyle A_{i}$$ and exactly 9 of the $$\displaystyle B_{j}$$. Then n is equal to-

Suppose $$\displaystyle A_{1},A_{2}.....A_{30}$$ are thirty sets having 5 elements and $$\displaystyle B_{1},B_{2}....B_{n}$$ are n sets each with 3 elements. Let $$\displaystyle \bigcup_{i=1}^{30}Ai=\bigcup_{i=1}^{n}Bj=S$$ and each elements of S belongs to exactly 10 of the Ai's and exactly 9 of the Bj's. Then n is equal to 

S = {1, 2, 3, 5, 8, 13, 21, 34}. Find $$\displaystyle \sum max\left ( A \right )$$ where the sum is taken over all 28 two elements subsets A to S

Given n(A) = 11, n(B) = 13, n(C) = 16, $$\displaystyle n\left ( A\cap B \right )=3,n\left ( B\cap C \right )=6,n\left ( A\cap C \right )=5\: \: and\: \: n\left ( A\cap B\cap C \right )=2$$ then the value of $$\displaystyle n [ A\cup B \cup C ]=$$