Discrete Mathematics
# Set Operations

**Details:**

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

**True or False?**

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

If **X** and **Y** are two sets, **X \(∩\) \((Y∪X)^c\)** is equal to

**Details** **and** **assumptions**:

\(\rightarrow\) **\(∩\)** represents intersection.

\(\rightarrow\) **\(∪\)** represents union.

\(\rightarrow\) \(X^c\) represents compliment of set X.

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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