Statements and Truth Values
A proposition is true or false, never both.
Key idea
A proposition is true or false, never both.
In depth
A statement (proposition) is a sentence that is definitely true or false. Questions, commands and open sentences like "x > 3" are not statements until x is specified. Logic studies how truth values combine.
Worked example
"7 is prime" is true; "9 is prime" is false; "Close the door" is not a statement.
Real-world uses
- Checking whether a rule in a contract or a code condition is true for a given case
Common mistake
Treating an expression with an unspecified variable as a statement.
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 Statements and Truth Values?
A proposition is true or false, never both. It is a topic at the intermediate level in Discrete Math & Number Theory.
Where is Statements and Truth Values used in real life?
Real-world examples: Checking whether a rule in a contract or a code condition is true for a given case.
What should I learn before Statements and Truth Values?
It is the first topic in Discrete Math & Number Theory, so no earlier topic in this area is needed.
What is a common mistake with Statements and Truth Values?
Treating an expression with an unspecified variable as a statement.
How can I practise Statements and Truth Values?
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 Statements and Truth Values?
Move on to Logical Connectives next.
Related intermediate topics in Discrete Math & Number Theory
- Logical Connectives – AND, OR, NOT, implication and biconditional.
- Truth Tables – List all truth assignments to evaluate compound statements.
- 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.