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Consider U = {x|x is a negative real number}.
Which is an empty set?
O {x|x e U and x has a negative cube root}
O {x\X EU and x has a negative square root}
O {x|x e U and x is equal to the product of a positive number and -1}
O {x|x EU and x is equal to the sum of one negative and one positive number}

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Answer:

{x\ x e U and x has a negative square root} is an empty set.

Step-by-step explanation:

If x e U, x is a negative real number, and they don't have a square root (they don't have even roots). Their square roots are complex numbers, not real ones.

Answer:

Option B.

Step-by-step explanation:

Consider,

[tex]U=\{x|x\text{ is a negative real number }\}[/tex]

We need to find the empty set from the given options.

In option A,

Let [tex]S_1=\{x|x\in U\text{ and }x \text{ has a negative cube root}\}[/tex]

Since x has a negative cube root, it means x is a negative real number. So, this set is not an empty set.

In option B,

Let [tex]S_2=\{x|x\in U\text{ and }x \text{ has a negative square root}\}[/tex]

Since x has a negative square root, it means x is a positive real number because square root of a negative number is an imaginary number. So, this set is an empty set.

In option C,

Let [tex]S_3=\{x|x\in U\text{ and }x \text{ is equal to the product of a positive number and -1}\}[/tex]

Since x is equal to the product of a positive number and -1, it means x is a negative real number. So, this set is not an empty set.

In option D,

Let [tex]S_4=\{x|x\in U\text{ and }x \text{ is equal to the sum of one negative and one positive number}\}[/tex]

Since x is equal to the sum of one negative and one positive number, it means x can be a negative real number or positive real number. So, this set is not an empty set.

Hence, option B is correct.

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