Set Theory Test...

Which of the following statements is true

Let $$P = \{ x | x$$ is a multiple of $$3$$ and less than $$100 $$ ,$$x$$ $$\displaystyle \in $$ $$N \}$$
$$Q = \{ x | x$$ is a multiple of $$10$$ and less than $$100$$, $$x$$ $$\displaystyle \in$$ $$N\}$$

Find the set of all solutions of the equation $$2^{\left | y \right |}-\left | 2^{y-1}-1 \right |=2^{y-1}+1$$, the solution includes

If X and Y are two sets then $$\displaystyle X\cap (Y\cup X)'$$ equals:

If $$Q=\{ x:x=\cfrac { 1 }{ y },$$ where $$ y\in N \} $$, then

$$\displaystyle A=\left\{ x:x\neq x \right\} $$ represents:

Which of the following statements is true ?

Given $$\displaystyle \xi $$ = {x : x is a natural number}
A = {x : x is an even number x $$\displaystyle \in $$ N}
B = {x : x is an odd number, x $$\displaystyle \in $$ N}
Then $$\displaystyle (B\cap A)-(x-A)=....$$

If n (A) = 120, N(B) = 250 and n (A - B) = 52, then find $$\displaystyle n(A\cup B)$$

The solution set of $$x+2<9$$ over a set of positive even integers is