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Logic lab: propositions and truth tables

Computers, lawyers and mathematicians all use logic. Fill in truth tables and find out when an “if … then” statement is really true.

🧠p → q ≡ ¬q → ¬plogic and truth tables
LevelS4 (and A Level)
TimeAbout 35 min
You useTruth tables
PriceFree: no account

🎯 Aim

To use truth tables to evaluate compound statements and test logical equivalence.

You will learn to

  • Use the connectives ∧, ∨, ¬, → and ↔.
  • Build truth tables.
  • Identify tautologies and equivalent statements.
  • Write the converse and contrapositive.

🧭 What to do

  1. Choose a Statement.
  2. Tap each cell to choose T or F, then Check my table.
  3. Compare ¬(p ∧ q) with ¬p ∨ ¬q.
  4. Choose sentences for p and q and read the contrapositive.
  5. Answer the questions with the class data.
  6. Write your conclusion and download your lab report.

🔬 Lab bench

📋 The data

Truth tables of the main connectives.

🧠 Investigate: answer from the data

Type your answer and tap Check. Use 💡 Hint first; open the method only when you are stuck.

📄 My lab report

Your report collects the aim, your data table, the graphs, your answers and your conclusion. It is made on your phone or computer: nothing is sent to anyone.

Check your conclusion

A truth table lists every combination of truth values (2ⁿ rows for n propositions). p → q is false only when p is true and q false. ¬(p ∧ q) and ¬p ∨ ¬q have the same truth table (De Morgan), and an implication is equivalent to its contrapositive but not to its converse. The same rules run the logic gates in computers.

➕ Get more from this experiment

📝 Free

Print the worksheet (button above), download the data, and save your report. Teachers can project this page in class.

📦 Premium Lab Pack

1 000 RWF

  • Worksheet: logic puzzles and truth tables
  • Logic problems
  • Teacher guide and answer key
  • Exam-style questions with marking scheme

👩‍🏫 For teachers

Use it as a practical when apparatus is missing, as homework, or as a project. Free lesson plans help you plan, teach and assess.

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