Answer
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
A \cup (B - C) = (A \cup B) - (A \cup C) \\
this\,\,is\,\,false:\\
counter\,\,example\,\,:\\
A=\left \{ 1 \right \},B=\left \{ 2 \right \},C=\left \{ 3 \right \}\\
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
A \cup (B - C) = (A \cup B) - (A \cup C) \\
this\,\,is\,\,not\,\,true:\\
counter\,\,example\,\,:\\
A=\left \{ 1 \right \},B=\left \{ 2 \right \},C=\left \{ 3 \right \}\\
B-C=\left \{ 2 \right \}\\
L.H.S:\\
A\cup (B-C)=\left \{ 1 \right \}\cup \left \{ 2 \right \}=\left \{ 1,2 \right \}\\
A\cup B=\left \{ 1,2 \right \},A\cup C=\left \{ 1,3 \right \}\\
R.H.S\\
(A\cup B)-\left ( A\cup C \right )=\left \{ 1,2 \right \}-\left \{ 1,3 \right \}=\left \{ 2 \right \}\\
A \cup (B - C)\neq (A \cup B) - (A \cup C)\\ (\left \{ 1,2 \right \}\neq \left \{ 2 \right \})$
