RTUComputer ScienceYr 2024 · Sem 42024

Q5Discrete Mathematics Structure

Question

2 marks

Explain Quantifiers. Also write properties of quantifiers.

Answer

Quantifiers specify the extent to which a predicate applies to a domain.

Quantifiers are operators that specify the range or scope of a variable in a logical expression. There are two primary types:

Universal Quantifier ( $\forall$ ): States that the property holds for all elements in the domain.
Existential Quantifier ( $\exists$ ): States that there exists at least one element in the domain for which the property holds.

Properties:

$\sim (\forall x, P (x)) \equiv \exists x, \sim P (x)$ (De Morgan's for quantifiers)
$\sim (\exists x, P (x)) \equiv \forall x, \sim P (x)$