Proof by deduction
What Proof by deduction means in Mathematics A-Level, as defined for AQA, Pearson Edexcel, WJEC.
Definitions of Proof by deduction
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Reference: WJEC
Starts with clear algebraic definitions, such as an even integer expressed as 2k and an odd integer as 2k + 1 for k ∈ ℤ, and uses algebraic expansion and factorisation to demonstrate closure.
Uses algebra or known results to show a statement is always true, for example completing the square to prove x² + 4x + 7 > 0 for all real x.
Uses algebra or known results to show a statement is always true, proceeding from given assumptions through logical steps to a conclusion.
A proof method that uses definitions and valid logical or algebraic steps to establish a result for every value in the stated domain.
Topics that use Proof by deduction
- A: Proof (AQA A-Level)
- Proof (Pearson Edexcel A-Level)
- Overarching themes - Mathematical argument, language and proof (WJEC A-Level)
- Proof (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
Related terms
- Proof by exhaustion
- Proof
- counter-example
- Disproof by counter example
- Irrational Number
- Proof by contradiction
- Rational Number
- Domain
Using Proof by deduction in the exam
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