Question

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

Which is an empty set?


x ∈ U and 1/2 x is prime


x ∈ U and 2x is prime


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


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

Answer 1

x

Explanation:

got 100%

Answer 2

Answer: x is an empty set.

Justification:

U = x = {2, 3, 4, 5, 6, ...}


1) x

Take x = 4 => (1/2) 4 = 4 / 2 = 2 = prime, so this is not empty.


x ∈ U and 2x is prime

2) 2x = {4, 6, 8, 10, 12, } so none of them is prime, hence this is an empty set.

3) x

Take any x that is odd. For example x = 3

=> (1/2)x = (1/2)3 = 3/2 which is a fraction, so this is not an empty set.


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

Take any value of x, for example x = 7 => 2 = 14, and 14 = 28 / 2 so this is not an empty set.