First slide

Operations on Sets

Question

$Let A and B be two sets, then (A \cup B)^{C} \cup (A^{C} \cap B) equals$

Moderate

A

$A^{c}$
B

$B^{c}$
C

$A$
D

None of these

Solution

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

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