Consider u = {x|x is a positive integer greater than 1}. which is an empty set?

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 484 People

Consider U = {x|x is a positive integer greater than 1}.
Which is an empty set?

{x|x ∈ U and 1/2 x is prime}

{x|x ∈ U and 2x is prime}

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

{x|x ∈ U and 2x can be written as a fraction}

Answered by maham237 @ 27/12/2020

B) {x|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.

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