Waste less time on Facebook — follow Brilliant.
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.
Set Operations
Familiarize yourself with the foundational notation, tools and concepts for the operations that are applied to sets.
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
Consider the sets \[\begin{align} A &=\{x \mid -8 < x < 4, x \text{ is an integer} \}\\ B &=\{x \mid -2 < x \leq 11, x \text{ is an integer} \}. \end{align}\] What is \( \lvert A \triangle B \rvert ?\)
Details and assumptions
You may choose to read the summary page 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.
Consider two sets:
\[ A = \{ 5, 6, 7, 8, 9, 10 \} \\ B = \{ 6, 8, 10, 16, 24 \} \]
What is \( \lvert A \triangle B \rvert \)?
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.
Consider the sets \[A=\{1,2,a+7\}, B=\{a+3, a^2, -a+10, 16\}.\] If \(A \cap B=\{1, 16\},\) what is the sum of all the elements in the set \(A \triangle B?\)
Details and assumptions
You may choose to read the summary page 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.
If sets \(A\) and \(B\) satisfy \[\begin{align} A & =\{23, 11, 55, 6, 4, 18, 37 \},\\ A\cap B & =\{37, 55\}, \\ \lvert A \triangle B \rvert & =5, \end{align}\] what is the sum of all the elements in the set \(B?\)
Details and assumptions
You may choose to read the summary page 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.
If \(A\) and \(B\) are two sets such that \[|A|=24, |B|=17, |B-A|=9,\] what is the value of \( \lvert A \triangle B \rvert ?\)
Details and assumptions
You may choose to read the summary page Set Notation.