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

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If $A = \{$1, 7, 12, 18, 20$\}$, $B = \{$3, 7, 11, 16, 18$\}$ and $C = \{$1, 3, 18, 22$\}$, then prove De Morgan's law of set difference and hence determine $(A - B) \cap (A - C)$.

1. De Morgan's law of set difference:

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

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

$\{1, 3, 7, 11, 16, 18, 22\}$
$\{7, 12, 20\}$
$\{1, 12, 20\}$
$\{12, 20\}$

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5. Prove De Morgan's law for set difference

Exercise condition: