Constructing Mathematical Arguments

Constructing a mathematical argument means building a chain of logical reasoning from given premises to a conclusion. This goes beyond simply performing calculations — it requires precision in language, clarity of structure, and rigorous use of logic. The AQA A-Level Mathematics specification (7357) emphasises that students should "construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language."

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Logical Connectives

Mathematical arguments use logical connectives to link statements together. Understanding these is essential for constructing and reading proofs.

"And" (∧)

The statement "A and B" (written A ∧ B) is true only when both A and B are true.

Example: "n is even and n > 10" means n must satisfy both conditions (e.g., n = 12 works, but n = 8 and n = 13 do not).

"Or" (∨)

In mathematics, "A or B" (written A ∨ B) is true when at least one of A or B is true (this is the inclusive or).