Discrete Mathematics
# Set Operations

What is \(|A^{C}\cup B^{C}|\)?

**Details:**

\(|S|\) represents the cardinality of the set \(S\) and \(S^C\) represents the complement of the set \(S\).

**True or False?**

\[\left|X^C \cup Y^C \cup Z^C\right| = \left|(X \cap Y \cap Z)^C\right|\]

**True or false**:

\(\quad \) There exist three nonempty sets \(A\), \(B\), and \(C\) such that

\(\quad \) \(A\cup (B-C)\neq (A\cup B)-(A\cup C)\).

In my fridge's shelves there are 10 condiments that are good for breakfasts, 8 that are good for lunch/dinner, and 12 that are good for dessert.

Of all of the condiments, exactly half of those that are good for breakfast are also good for lunch/dinner. And every condiment is either good for desert or good for *both* lunch/dinner *and* breakfast.

Given all of this, what is the ** difference** between the

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