Q14 / 35 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sets and Relations

For any two sets $A$ and $B,$ the values of ${[(A - B) \cup B]}^{C}$ is equal to

Correct answer
A
$A^{C} \cap B^{C}$
B
$A \cup B$
C
$A - B$
D
$B - A$

Solution

\begin{array}{l} (A - B) \cup B = (A \cap B^{C}) \cup B \\ = (A \cup B) \cap (B^{C} \cup B) \\ = (A \cup B) \cap (U) \\ = A \cup B \end{array}

Hence,

{[(A - B) \cup B]}^{C} = {(A \cup B)}^{C} = A^{C} \cap B^{C}

Hence, the correct answer is option: 'A'.

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