Question

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

Which is an empty set?

x ∈ U and 1/2x is prime
x ∈ U and 2x is prime
x
x ∈ U and 2x can be written as a fraction

Answer 1

`2x` will be an even number, which means it's immediately divisible by 2. Therefore it cannot be prime, so the second set is empty.

Answer 2

Hence, the set that is empty is:

x ∈ U and 2x is prime

Explanation:

We are given:

U = 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 ∈ 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.