Skills: Parsing formulas with ∀ and ∃, Identifying free vs. bound variables, Applying ∀-elimination correctly, Translating simple English sentences into predicate logic
Skills: Applying ∃-introduction, Applying ∃-elimination with fresh constants, Tracking dependency conditions in quantified proofs, Diagnosing common mistakes with existential reasoning
Skills: Using identity (=) in formal proofs, Substitution of identicals, Reasoning about relations (order, parent, membership, etc.), Formalizing simple theories with predicates
Skills: Constructing first-order structures, Evaluating truth in a model, Finding countermodels to invalid arguments, Connecting semantic failure to proof-theoretic limitations
Skills: Combining quantifier rules in longer derivations, Checking freshness and dependency constraints, Moving between informal arguments and formal proofs, Preparing for the in-precept quiz