Question

Consider U = {x|x is a negative real number}.

Answer 1

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 2

Answer:

Option B.

Step-by-step explanation:

Consider,

$U=\{x|x\text{ is a negative real number }\}$

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

In option A,

Let $S_1=\{x|x\in U\text{ and }x \text{ has a negative cube root}\}$

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 $S_2=\{x|x\in U\text{ and }x \text{ has a negative square root}\}$

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 $S_3=\{x|x\in U\text{ and }x \text{ is equal to the product of a positive number and -1}\}$

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 $S_4=\{x|x\in U\text{ and }x \text{ is equal to the sum of one negative and one positive number}\}$

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.