Proof by Direct Argument
Derive the conclusion from premises with valid steps.
Key idea
Derive the conclusion from premises with valid steps.
In depth
Start from the hypothesis and deduce the conclusion through logical steps using definitions and known results. It is the most natural proof style: assume p, derive q.
Worked example
Claim: the sum of two even numbers is even. Let a = 2m, b = 2n; then a + b = 2(m + n), which is even.
Real-world uses
- Showing a sum of two even numbers is even in exams and in writing formal arguments
Common mistake
Using an example instead of a general argument.
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 Proof by Direct Argument?
Derive the conclusion from premises with valid steps. It is a topic at the advanced level in Discrete Math & Number Theory.
Where is Proof by Direct Argument used in real life?
Real-world examples: Showing a sum of two even numbers is even in exams and in writing formal arguments.
What should I learn before Proof by Direct Argument?
Make sure you are comfortable with Negating Quantified Statements, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Proof by Direct Argument?
Using an example instead of a general argument.
How can I practise Proof by Direct Argument?
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 Proof by Direct Argument?
Move on to Proof by Contrapositive next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- De Morgan’s Laws – Negation swaps AND and OR.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.