Question

Let S(x) denote "x obeys the speed limit," where the domain is the set of all drivers. Express the negation of the proposition "Some drivers do not obey the speed limit" using quantifiers, and then express the negation in English.

Answer 1

Using Quantifiers: ¬∃x¬S(x)≡ ∀xS(x)

English Language: All drivers obey the speed limit

Explanation:

The domain is the set of all drivers i.e. the domain of drivers

Let S(x) be the predicate “x obeys the speed limit.”

The above statement can be written as ∃x¬S(x),

The negation is represented by ¬∃x¬S(x)≡ ∀xS(x)

In English Language, it is ->, all drivers obey the speed limit