Discrete Mathematics
# Set Operations

$|A^{C}\cup B^{C}|$?

What is**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