Set Operations
Details:
\(|S|\) represents the cardinality of the set \(S\) and \(S^C\) represents the complement of the set \(S\).
by
Chung Kevin
True or False?
\[\left|X^C \cup Y^C \cup Z^C\right| = \left|(X \cap Y \cap Z)^C\right|\]
by
Zandra Vinegar
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.
by
Akhil Bansal
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?
by
Clara Blackstone
If \(A\) and \(B\) are subsets of \(U=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}\) such that \[ { A }^{ c }\cap { B }^{ { c } }=\{1, 9\}, A\cap B =\{2\}, { A }^{ c }\cap B=\{4, 6, 8\},\] what is the set \(A?\)
by
Lawahar Qasid