Question

Consider U = {x|x is a positive integer greater than 1}.

Which is an empty set?

{x|x ∈ U andOne-half is prime}
{x|x ∈ U and 2x is prime}
{x|x ∈ U andOne-half can be written as a fraction}
{x|x ∈ U and 2x can be written as a fraction}

Answer 1

Sets 1 and 2 are empty.

- {x ∈ U | one-half is prime}: the statement "one-half is prime" is false, so no x satisfy it.
- {x ∈ U | 2x is prime}: for x>1, 2x is an even integer >2, hence not prime, so no x satisfy it.

Sets 3 and 4 are not empty (their conditions are true for all x in U).