First slide

Operations on Sets

Question

For sets A and B, $(A \cup B)^{'} \cup (A^{'} \cap B)$ equals

Moderate

A

A'
B

B'
C

A
D

None of these

Solution

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

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