Logic

Quantifiers, contrapositives, and arguments that hold up.

Logic is the grammar of proof. Every other category leans on it, and it is worth practising on its own, where the reasoning is the entire content of the problem rather than the scaffolding around it.

You will find propositional and predicate logic, negation and contraposition, quantifier order, truth tables, and puzzles about consistent and inconsistent statements. Precision matters more than speed here.