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State the Cantor-Schröder-Bernstein Theorem.
State the Cantor-Schröder-Bernstein Theorem.
If there exist injections $f: A \rightarrow B$ and $g: B \rightarrow A$, then there exists a bijection $h: A \rightarrow B$.
What is an uncountable set? Provide an example.
What is an uncountable set? Provide an example.
An uncountable set is a set that cannot be put in one-to-one correspondence with the natural numbers. An example is the set of real numbers.
Explain the Inclusion-Exclusion principle in combinatorics.
Explain the Inclusion-Exclusion principle in combinatorics.
The Inclusion-Exclusion principle is a counting technique used to find the number of elements that belong to at least one of several sets, by subtracting the intersections of different sets.
Define equivalence relation on a set.
Define equivalence relation on a set.
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How does the Pigeonhole Principle apply in combinatorics?
How does the Pigeonhole Principle apply in combinatorics?
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