Set Theory Test...

If A is a finite set, let $$P(A)$$ denote the set all subsets of A and $$n(A)$$ denote the number of elements in A. If for two finite sets X and Y, $$n[P(X)] = n[P(Y)] + 15$$ then find $$n(X)$$ and $$n(Y)$$

If A and B are two sets, where A has more elements than B. Calculate the least possible value of n(A) + n(B), where n(A) is the number of elements in A and n(B) is the number of elements in B.

Solve the following inequalities: $$\displaystyle\frac{1}{2-|x|}\geq 1$$.

Let $$S = \left \{(a, b, c)\epsilon N\times N\times N : a + b + c = 21. a \leq b\leq c\right \}$$ and $$T = \left \{a, b, c)\epsilon N\times N\times N : a, b, c,\ are\ in\ A.P.\right \}$$, where $$N$$ is the set of all natural numbers. Then the number of elements in the set $$S\cap T$$ is

Which one of the following is correct?

Which one of the following is a finite set?

If $$X=\left \{ a,\left \{ b,c \right \},d \right \}$$, which of the following is a subset of $$X$$?

If $$A=\left \{ 5,\left \{ 5,6 \right \},7 \right \}$$, which of the following is correct? 

The number of subsets of the set $$\left \{ 10,11,12 \right \}$$ is

If $$n(A) = 20, n(B) = 30$$ and $$n(A \cup B)= 40$$, then $$n(A \cap B)$$ is equal to: