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Probability

Set Operations

Concept Quizzes

Union and Intersection
Sets - Complement
Sets - Relative Complement
Sets - Symmetric Difference
Sets - Composition of Operations
Sets - Operations on Multiple sets

Challenge Quizzes

Set Operations: Level 1 Challenges
Set Operations: Level 2 Challenges

Set Operations: Level 1 Challenges

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 $S$ .

9 4 8 5

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by Chung Kevin

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True or False?

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

True False There isn't enough information

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by Zandra Vinegar

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True or false:

$\quad$ There exist three nonempty sets $A$ , $B$ , and $C$ such that
$\quad$ $A\cup (B-C)\neq (A\cup B)-(A\cup C)$ .

True False

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by Shawn Franchi

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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?

18 0 Given what we know, there could be infinitely many condiments, so "infinity!" 4 5

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by Clara Blackstone

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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 $A?$

\{1, 2, 6, 7\}

\{5, 8\}

\{2, 3, 5, 7\}

\{3, 4, 9\}

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by Lawahar Qasid

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