Florida B.E.S.T. MA.912.LT.4.5

MathGrades 9–12Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

The Standard

Determine whether two propositions are logically equivalent.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students build truth tables for compound statements and compare the final columns. They may also apply laws such as De Morgan’s laws to show that two forms always match.
What Mastery Looks Like: A student can test every possible truth-value assignment and compare the final columns accurately. The student states whether the expressions match in every case and supports the conclusion with clear work.
Common Misconceptions: Students often check only one truth-value case instead of every possible case. They may confuse a converse with a contrapositive or negate and, or, and conditional statements incorrectly.
How to Assess It: Exit ticket: Use a truth table to decide whether ¬(p ∧ q) and ¬p ∨ ¬q are equivalent. Justify your answer in one sentence.

Lesson moves

Have pairs arrange T and F cards for two variables, then build and compare compound statement columns on chart paper.
Ask students to explain why checking one matching truth-table row cannot prove equivalence.
Run a matching game where students pair expression cards with equivalent truth tables or logical forms.
Translate a store return policy into symbols, then compare the policy with its contrapositive using a truth table.

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