<h3><u>
Answer:</u></h3>
Hence, the set that is empty is:
{x|x ∈ U and 2x is prime}
<h3><u>
Step-by-step explanation:</u></h3>
We are given:
U = {x|x is a positive integer greater than 1}
i.e. U={2,3,4,5,6,7,.....}
The empty set among the following is:
{x|x ∈ U and 2x is prime}
As x ∈ U.
This means that x has to be an positive integer which is greater than 1.
and 2x will be an even integer i.e. {4,6,8,.....}.
Hence,
the term 2x can't be a prime as each of the number has more than 2 factors other than 1 and number itself.