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Math
Virginia Math
Discrete Mathematics: Set and Number Theory
Compare and contrast sets, relations, and functions.
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Express relationships between sets using Venn diagrams.
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Describe a set using set-builder notation.
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Construct new sets using the set operations intersection, union, difference, and complement.
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Identify the laws of set theory (e.g., associative, commutative, distributive, De Morgan’s Law).
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Use the principle of inclusion and exclusion to determine the size of a set.
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Use the properties of set operations to prove set equality.
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Create a tree diagram to represent relationships between independent events.
Use the Fundamental (Basic) Counting Principle to determine the number of possible outcomes of an event.
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Determine the number of combinations possible when subsets of 𝑟 elements are selected from a set of 𝑛 elements without regard to order.
Determine the number of permutations possible when 𝑟 objects selected from 𝑛 objects are ordered.
Use the pigeonhole principle to solve packing problems to facilitate proofs.
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Construct a proof by induction using principles of combinatorics.
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Construct Pascal’s Triangle.
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Expand binomials having positive integral exponents, using the Binomial Theorem and Pascal’s Triangle.
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Compare the binomial coefficient to the calculation of combinations.
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Identify the Fibonacci numbers within Pascal’s Triangle.
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