Florida B.E.S.T. MA.912.LT.5.6
The Standard
Prove set relations, including DeMorgan’s Laws and equivalence relations.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students show that two set expressions contain exactly the same elements, using membership statements, logical steps, or two containments. They also check whether a relation is reflexive, symmetric, and transitive, then describe the resulting classes.
What Mastery Looks Like
- A student can begin with an arbitrary element and write a correct if-and-only-if chain from one set expression to another. Given a relation rule, the student proves all three properties and identifies its classes. If a property fails, the student gives a specific counterexample.
Common Misconceptions
- Students often negate a union without changing it to an intersection, or complement only one set. They may test a few examples instead of using an arbitrary element, and may confuse symmetric with transitive.
How to Assess It
- Exit ticket: Prove that the complement of A union B equals the intersection of their complements. Then justify whether a ~ b when a − b is even gives an equivalence relation on the integers.
Lesson moves
Ways to Teach It
Place labeled student cards inside overlapping yarn loops, then physically build complements, unions, and intersections to test both DeMorgan identities.
Ask students to explain why proving two sets equal requires both inclusions, then write an arbitrary-element proof for one identity.
Run a relation sort where teams classify cards as reflexive, symmetric, transitive, or equivalent, earning points with a proof or counterexample.
Group calendar dates by weekday modulo 7, then show how the grouping rule creates nonoverlapping equivalence classes.
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Related Standards
- MA.912.LT.5.5
Explore relationships and patterns and make arguments about relationships between sets using Venn Diagrams.
- MA.912.LT.5.3
Partition a set into disjoint subsets and determine an equivalence class given the equivalence relation on a set.
- MA.912.GR.1.4
Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelog...
- MA.912.GR.1.3
Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
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