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

Which is an empty set?

x

x ∈ U and 2x is prime

x

x ∈ U and 2x can be written as a fraction

B) x ∈ U and 2x is prime

x is greater than 1.

the only even prime number is 2

2 times anything is even.

the minimum x value is 2. 2x is 4, therefore higher than the only even number

every value 2x will have a multiple of 2 so it will not be prime.

I think it's 1/2x is prime because half of a prime number cannot be a whole number.