Prove De Morgan's law for set difference — task. Mathematics State Board, Class 9.

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If $A = \{$0, 7, 12, 19, 21$\}$, $B = \{$5, 7, 11, 14, 19$\}$ and $C = \{$0, 5, 19, 22$\}$, then prove De Morgan's law of set difference and hence determine $(A - B) \cup (A - C)$.

1. De Morgan's law of set difference:

$A - (B \cup C) = (A - B) \cup (A - C)$
$A - (B \cap C) = (A - B) \cap (A - C)$
$A - (B \cap C) = (A - B) \cup (A - C)$
$A - (B \cap C) = (A - B) \cup (B - C)$

2. $(A - B) \cup (A - C)$

$\{7, 12, 21\}$
$\{5, 19\}$
$\{0, 7, 12, 21\}$
$\{0, 12, 21\}$

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5. Prove De Morgan's law for set difference

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