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Lesson subsection

Truth Tables & Logical Equivalence

Read the explanation, try the on-paper prompts, then explain the idea in your own words. Use AI feedback as a mentor, not a shortcut.

10–20 min focusProof-first mindset

Best flow: read → think on paper → write a short explanation → refine with feedback.

Reading

Core explanation

Truth tables let us analyze compound logical statements by listing all possible truth values.

Two statements P and Q are logically equivalent if they always have the same truth value.

Key examples:

  • P → Q is equivalent to ¬P ∨ Q.
  • P ↔ Q is equivalent to (P → Q) ∧ (Q → P).
  • Double negation: ¬(¬P) is equivalent to P.

Truth tables are a mechanical tool to verify these equivalences.

TL;DR — key idea

Truth tables measure truth under all conditions. Logical equivalence means two statements behave identically in every case.

Try these in your notebook

Don’t skip this – writing proofs or explanations on paper is where most of the learning actually happens.

  • 1

    Construct a truth table for the expression ¬P ∨ Q. Is it logically equivalent to P → Q? Explain why or why not.

Once you’ve sketched some ideas, summarize the main insight in the reflection box on the right.

Check your understanding

In 3–6 sentences, explain the core idea of this subsection as if you were teaching a friend who hasn’t seen it. Focus on the logic, not just the final statements.

AI is optional. Use it to spot gaps and sharpen your wording, not to replace your own thinking.