Question

Translate the quantification into English and determine its truth value.
∃x∈R(x³=−1)

Answer 1

The quantification ∃x∈R(x³=-1) can be translated as "There exists a number x in the set of real numbers such that x cubed is equal to negative one." The truth value of this quantification is true, as there exists a real number (-1) that satisfies the equation x³ = -1.

Step-by-step explanation:

The given quantification, ∃x∈R(x³=−1), can be translated into English as "There exists a number x in the set of real numbers such that x cubed is equal to negative one."

To determine its truth value, we need to check if there is at least one real number whose cube is equal to negative one. In this case, the equation x³ = -1 has a solution. The real number that satisfies this equation is x = -1. Therefore, the quantification is true, as there exists a real number (-1) that makes x³ equal to -1.