Question

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

Which is an empty set?

{x|x ∈ U and x has a negative cube root}
{x|x ∈ U and x has a negative square root}
{x|x ∈ U and x is equal to the product of a positive number and –1}
{x|x ∈ U and x is equal to the sum of one negative and one positive number}

Answer 1

{x | x ∈ U and x has a negative square root} is empty.

Reason: no negative real number has a real square root. (By contrast every negative real has a negative cube root, every negative real equals (-1) times a positive number, and every negative real can be written as the sum of one negative and one positive number.)