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Excel in math and science
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Set Notation
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Concept Quizzes
Which flag would be in the same category as that of South Korea?
Excel in math and science
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It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
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Given the sets \[ \begin{align} U &=\{1,2,3,\ldots,8\},\\ A &=\{X \mid 8 \in X, X \subseteq U\},\\ B &=\{Y \mid 1 \in Y, Y \subseteq U\}, \end{align}\] what is \(\lvert{A \cup B}\rvert?\)
Details and assumptions
\(\lvert{S}\rvert\) denotes the number of members of the set \(S.\)
Excel in math and science
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Let \(B\) be a subset of the set \[A=\{1,2,3,4,5,\ldots,n\}\] such that \(1\) and \(2\) are elements in \(B\) but \(3\) and \(4\) are not. If there are a total of \(128\) such subsets \(B\), what is the value of \(n?\)
Excel in math and science
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It's hard to learn from lectures and videos
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Our wiki is made for math and science
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In counting the numbers from 1 to 99 (inclusive), what is the total number of times that the digit 3 is used?
Details and assumptions
The number \(12\) uses the digit 1 once and the digit 2 once.
The number \(111\) uses the digit 1 three times.
Excel in math and science
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Given the set \(U=\{x \mid x \text{ is a positive integer } \leq 12\},\) let \(A=\{2, 4\}\) and \(B=\{2, 6, 9, 11, 12\}\) be two subsets of \(U.\) How many sets \(X\) are there such that \[\begin{align} \text{I}&. && X \subseteq U, \\ \text{II}&. && |B \cap X|=3, \\ \text{III}&. && A \text{ and } X \text{ are mutually disjoint?} \end{align} \]
Details and assumptions
You may choose to read the summary page Set Notation.