Discrete Mathematics

Set Operations

Set Operations: Level 1 Challenges

         

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

Details:

S|S| represents the cardinality of the set SS and SCS^C represents the complement of the set SS.

True or False?

XCYCZC=(XYZ)C\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 AA, BB, and CC such that
\quad A(BC)(AB)(AC)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 maximum number of condiments that I might have in my fridge and minimum number of condiments that I might have in my fridge?

If AA and BB are subsets of U={1,2,3,4,5,6,7,8,9}U=\{1, 2, 3, 4, 5, 6, 7, 8, 9\} such that AcBc={1,9},AB={2},AcB={4,6,8}, { A }^{ c }\cap { B }^{ { c } }=\{1, 9\}, A\cap B =\{2\}, { A }^{ c }\cap B=\{4, 6, 8\}, what is the set A?A?

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