Ask Question
10 August, 11:29

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}

+5
Answers (2)
  1. 10 August, 11:47
    0
    Answer: I think it's B. On edge.
  2. 10 August, 11:52
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers