ExamGOAL
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44

The set $\{x \in R: 1 \leq x<2\}$ can be written as ............. .

Explanation

The set $\{x \in R: 1 \leq x<2\}$ can be written as $(1,2)$.

45

When $A=\phi$, then number of elements in $P(A)$ is .............. .

Explanation

$$\begin{aligned} \therefore \quad & A =\phi \quad \Rightarrow n(A)=0 \\ & n\{P(A)\} =2^{n(A)}=2^0=1 \end{aligned} $$ So, number of element in $P(A)$ is 1 .

46

If $A$ and $B$ are finite sets, such that $A \subset B$, then $n(A \cup B)$ is equal to ............ .

Explanation

If $A$ and $B$ are two finite sets such that $A \subset B$, then $n(A \cup B)=n(B)$.

47

If $A$ and $B$ are any two sets, then $A-B$ is equal to ............. .

Explanation

If $A$ and $B$ are any two sets, then $A-B=A \cap B^{\prime}$

$\therefore \quad A-B=A \cap B^{\prime}$

48

Power set of the set $A=\{1,2\}$ is ........... .

Explanation

$$\therefore A=\{1,2\}$$

So, the subsets of $A$ are $\phi,\{1\},\{2\}$ and $\{1,2\}$.

$$\therefore \quad P(A)=\{\phi,\{1\},\{2\},\{1,2\}\}$$