Maths Question:
$\begin{align} & \text{Simplify } \\ & \text{i) }A\cup (A'\cap B) \\ & ii)A'\cap (A\cup B') \\ & iii)(A'\cap B')\cup (A\cap B) \\\end{align}$
Maths Solution:
$\begin{align} & b)\text{ Simplify } \\ & \text{i) }A\cup (A'\cap B)=(A\cup A')\cap (A\cup B)\text{ Distributive law} \\ & A\cup (A'\cap B)=\xi \cap (A\cup B)\text{ Law of complementation} \\ & A\cup (A'\cap B)=A\cup B\text{ Law of operation with }\xi \text{ and }\varnothing \\ & \\ & ii)A'\cap (A\cup B')=(A'\cap A)\cup (A'\cap B')\text{ Distributive law} \\ & \text{ }A'\cap (A\cup B')=\varnothing \cup (A'\cap B')\text{ Law of complementation} \\ & A'\cap (A\cup B')=A'\cap B'\text{ Law of operation with }\xi \text{ and }\varnothing \\\end{align}$
University mathstopic: