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Quantifier Duality: A Journey from ∀ (for all) to ∃ (exists)
Explore the simple relationship between forAll and exists using De Morgan’s Laws. Look at practical examples to see how understanding this relationship can help us write better and faster code. This is a step towards making coding more straightforward and more efficient.
© 2023 The Turing Taco Tales / Oscar Mauricio Forero Carrillo
Originally published at The Turing Taco Tales on October 25, 2023.
In logic and mathematics, quantifiers are the gatekeepers of generality and specificity. They enable us to make assertions about entire collections of objects. Among these quantifiers, ∀ ( for all) and ∃ ( exists) are the most important. Independent yet bound by an intriguing duality. We will refer to them using their mathematical symbols for brevity’s sake.
Relevant Logical Concepts
Before diving into the quantifiers’ connection, let’s review some relevant discrete logic concepts.
Predicate
A predicate is a statement about a subject. The statement can be over any property or condition of the subject. And it has to be true or false without any ambiguity. In programming, a predicate is a function that evaluates to true or false.
