Understanding quantified statements in mathematics learning at the university

Abstract

The objective is to provide knowledge for pure mathematics and mathematics education students to understand quantified statements so that they can easily comprehend the meaning of mathematical propositions and facilitate their proof. The method used in this research is a literature review by collecting various sources such as books or scientific writings related to the logic used to understand mathematics, specifically related to quantifiers, both universal and existential quantifiers. When mathematics and mathematics education students understand the quantified statement ∀x[Px], what they do is take any (cannot choose specific) x, and it must be proven that x satisfies property P. Then, to understand the quantified statement ∃x[Px], what is done is to choose (at least one) x, and it must be proven that x satisfies property P. When mathematics and mathematics education students understand the multi-quantifier statement ∀x∃y[P(x,y)], what is done is to take any (cannot choose specific) x, then find (at least one) y (depending on x), and x, y must satisfy property P. Then, to understand the multi-quantifier statement ∃y ∀x[P(x,y)] or ∃y [P(x,y)∀x], what is done is to choose y (independent of x) and it must be proven that y satisfies property P along with all x.