A course in Mathematical Logic

N: = set of natural numbers. R: = set of real numbers. x ∈ y: = x is an element of set y. {true, false}: = set of truth values. ∧: = connective “and”. ∨: = connective “or”. ¬: = connective “not”. →: = implication. ∀: = “for all ” or “every”. ∃: = “there exists ” or “some”. Propositional variable: = variable whose possible values are the truth values. Propositional formula: = either a propositional variable or A ∧ B, A ∨ B, A → B, ¬A, where A,B are propositional formulas. Tautology: = propositional formulas which is always true Universe: = set of elements where we interpret the constants, the function symbols an