If f: R \(\rightarrow\) R be defined as follows
\(f(x)=\begin{cases} 1,\quad \quad x\quad \in \quad Q \\ -1,\quad x\quad \notin \quad Q \end{cases}\)
Find  \(f\left( \frac { 1 }{ 2 } \right) ,f\left( \pi \right) \)

2

(a)

Show that n {P [P (P ( \(\phi\) ))]}=4

2

(a)

Let  B be a subset of an A and let P(A: B) = { X \(\in\) P(A): X \(\supset\) B}.
If A = (1,2,3,4} and B ={1,2}. List all the members of the set P(A :B).

2

(a)

Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions.
X  \(\subseteq\) B and X  \(\nsubseteq\) C

2

(a)

Let A = {1,2,3,4}, B= {1,2,3} and c= (2,4). Find all sets X satisfying each pair of conditions
X \(\subseteq\) B, X \(\neq\)B and X \(\nsubseteq\) C

2

(a)