Consider the following statement: x R such that x 2 = 2. Which of the following are

Chapter 3, Problem 14

(choose chapter or problem)

Consider the following statement:

\(\exists x \in \mathbf{R} \) such that \(x^{2}=2\).

Which of the following are equivalent ways of expressing this statement?

a. The square of each real number is 2.

b. Some real numbers have square 2.

c. The number x has square 2, for some real number x.

d. If x is a real number, then \(x^{2}=2\).

e. Some real number has square 2.

f. There is at least one real number whose square is 2.

Text Transcription:

exists x in mathbf R

x^2 =2