In the West, Aristotle put it as follows: "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true"
Some 2 millennia later, Tarski, a Polish logician, more or less formalised just that. This result, among other things, spawned a brand new branch in mathematics: Model Theory. More on Tarski’s notion of truth: https://plato.stanford.edu/entries/tarski-truth/. A few decades later some analytic philosophers like Davidson drew on Tarski’s work and applied it to natural language, too. This resulted in this: https://en.wikipedia.org/wiki/Truth-conditional_semantics. But notwithstanding Tarski’s work, there’s still significant controversy surrounding both “truth in natural language” and the logico-mathematical truth predicate in philosophical circles. Here’s an article that covers axiomatic theories of truth in general: https://plato.stanford.edu/entries/truth-axiomatic/.
You want to acquire and shoot for the so-called mathematical maturity. More precisely: to become an autonomous problem-solver and have the know-how to solve (non-)trivial proofs. Typically this means bridging the gap between computationally based maths which one is exposed to in pre-school to high-school years and sometimes in the first year of college/uni, and proof-based maths which involves and demands a good command of sets and operations on sets, quantifiers (universal, existential), logical operators (not, and, or, material conditional, biconditional), and proof methods (direct, indirect a.k.a reductio ad absurdum, induction, pigeonhole principle, etc.)
A good series of books aimed for pre-school and high-school students to accomplish just that is The Art of Problem Solving. Google it.