Direct proof

A direct proof derives the conclusion from assumptions using justified logical steps.

Different ways to understand it

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Bijections
A bijection is both injective and surjective and has a two-sided inverse.
Proof by contraposition
Proving not Q implies not P establishes the implication P implies Q.
Propositions
A proposition has a truth value; logical connectives build compound statements.
Sets
A set is a collection of distinct objects; membership is different from inclusion.
Axiomatic systems
An axiomatic theory derives theorems from stated axioms and inference rules.