If $U = \{1, 2, 3\}$ and $A = \{1, 2\}$ then $[P (A)]' = . . . . . . . . . . .$

$\{{3}, {2, 3}, {1, 3}, {1, 2}, ϕ\}$

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${{3}, {2, 3}, {1, 3}, {1, 2, 3}}$

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${{3}, {2, 3}, {1, 3}, {1, 2, 3}, ϕ}$

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${{3}, {2, 3}, {1, 3}, {1, 2}}$

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Solution

The correct option is B
${{3}, {2, 3}, {1, 3}, {1, 2, 3}}$

Explanation for the correct answer
Find the value of $[P (A)] ’$ :
$\begin{array}{rcl} U & = & \{1, 2, 3\} \\ P (U) & = & \{\{1\}, \{2\}, \{3\}, \{1, 2\}, \{2, 3\}, \{1, 3\}, \{1, 2, 3\}, ɸ\} \\ A & = & \{1, 2\} \\ [P (A)]' & = & \{\{3\}, \{2, 3\}, \{1, 3\}, \{1, 2, 3\}\} \end{array}$
Hence, B is the correct option.

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Similar questions

Which of the following is/are true?

1. If $A$ is a subset of the universal set $U$ , then its complement $A'$ is also a subset of $U$ .

2. If $U = \{1, 2, 3, \dots . ., 10\}$ and $A = \{1, 3, 5, 7, 9\}$ , then $(A')' = A$ .

U = {0, 1, 2, 3, 4}, A = {0, 2, 4}

B = {1, 2, 3}

U - B =

U = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

A = 1, 2, 3, 5

B = 2, 4, 6, 7

and C = 2, 3, 4, 8 . Then (B \cup C)^{'} is

U = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

A = 1, 2, 3, 5

B = 2, 4, 6, 7

and C = 2, 3, 4, 8 . Then (C - A)^{'} is

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {2, 5, 6, 9, 10}

A^{'}

If $U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; A = {1, 3, 5, 7, 9}$ and then find $A'$ also find $n (A')$ .

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