Set Notation

Concept Quizzes

Sets - Definition of terminology
Sets - Subsets
Sets - Classical Sets
Sets - Problem Solving

Challenge Quizzes

Set Notation: Level 2 Challenges
Cardinality: Level 3 Challenges

Sets - Problem Solving

Rakesh is classifying flags of the world according to the presence of red or blue in them.

Which flag would be in the same category as that of South Korea?

Bangladesh Greece Moldova Ireland

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by Brilliant Staff

Given the sets $\begin{aligned} U &=\{1,2,3,\ldots,8\},\\ A &=\{X \mid 8 \in X, X \subseteq U\},\\ B &=\{Y \mid 1 \in Y, Y \subseteq U\}, \end{aligned}$ what is $\lvert{A \cup B}\rvert?$

Details and assumptions

$\lvert{S}\rvert$ denotes the number of members of the set $S.$

320 256 192 384

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by Brilliant Staff

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 $n?$

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by Brilliant Staff

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.

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by Brilliant Staff

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 $\begin{aligned} \text{I}&. && X \subseteq U, \\ \text{II}&. && |B \cap X|=3, \\ \text{III}&. && A \text{ and } X \text{ are mutually disjoint?} \end{aligned}$

Details and assumptions

You may choose to read the summary page Set Notation.

64 256 63 128

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by Brilliant Staff