Truth Tables
List all truth assignments to evaluate compound statements.
Key idea
List all truth assignments to evaluate compound statements.
In depth
A truth table lists every combination of truth values for the variables and computes the truth of the whole expression. With n variables there are 2ⁿ rows. It is a complete, mechanical test.
Worked example
p → q is false only when p is true and q is false (row T, F); it is true in the other three rows.
Real-world uses
- Testing every input combination of a circuit or a security rule before deploying it
Common mistake
Missing rows, or forgetting that p → q is true when p is false.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Truth Tables?
List all truth assignments to evaluate compound statements. It is a topic at the intermediate level in Discrete Math & Number Theory.
Where is Truth Tables used in real life?
Real-world examples: Testing every input combination of a circuit or a security rule before deploying it.
What should I learn before Truth Tables?
Make sure you are comfortable with Logical Connectives, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Truth Tables?
Missing rows, or forgetting that p → q is true when p is false.
How can I practise Truth Tables?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Truth Tables?
Move on to Tautologies and Contradictions next.
Related intermediate topics in Discrete Math & Number Theory
- Statements and Truth Values – A proposition is true or false, never both.
- Logical Connectives – AND, OR, NOT, implication and biconditional.
- Subsets and Power Sets – A set with n elements has 2ⁿ subsets.
- Set Operations – Union, intersection, difference and complement.
- Venn Diagrams – Pictures of sets and their overlaps.
- Cartesian Products – All ordered pairs from two sets.