Consider U = x is a negative real number.

Which is an empty set?

XE U and x has a negative cube root

{x/X E U and x has a negative square root}

{x/x € U and x is equal to the product of a positive number and - 1}

{XIX E U and x is equal to the sum of one negative and one positive number}

x is an empty set.

Where U = x is a negative real number.

Step-by-step explanation:

Given U = x.

This set can be written as

U = {-1, - 2, - 3, ..., - 1000, ... }

Let us consider the options to see which one is an empty set.

(1) x has a negative cube root.

This is correct, as the cube root of any number in the set gives a negative value.

(-1) ³ = - 1 * - 1 * - 1 = - 1

(-2) ³ = - 2 * - 2 * - 2 = - 8

(-10) ³ = - 10 * - 10 * - 10 = - 1000

and so on.

So, x ∈ {-1, - 2, ..., - 10, ... }

This is not an empty set, it is not the correct option.

(2) x has a negative square root.

This is incorrect, as the square root of any number in that set gives a positive value.

(-1) ² = - 1 * - 1 = 1

(-2) ² = - 2 * - 2 = 4

(-9) ² = - 9 * - 9 = 81

and so on. This is the correct option as x ∈ U and x has a negative square root is an empty set.

(3) x is the product of one positive number and - 1.

This is correct.

-1 = 1 * - 1

-5 = 5 * - 1

-15 = 15 * - 1

and so on.

So, x ∈ {-1, - 2, ..., - 15, ... }This is not an empty set, it is not the correct option.

(4) x is the sum of one negative number and a positive number.

This is correct as

-1 = - 2 + 1

-4 = - 13 + 9

-50 = - 55 + 5

and so on.

So, x ∈ {-1, - 2, ..., - 50, ... }This is not an empty set, it is not the correct option.

Answer: I think it's B. On edge.