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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}

Respuesta :

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.

Empty sets are sets containing no elements. Out of given sets the empty set is given as: Option B: {x|x ∈ U and 2x is prime}

What is an empty set?

That set which doesn't contain any value is called empty set. This is also called as null set or void set. This is denoted by [tex]\phi[/tex] or { }

The given set U is:

U = {x|x is a positive integer greater than 1}

or

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

Checking all sets:

  • Case 1: S = {x|x ∈ U and 1/2 x is prime}

If we take 4 from U, then its half 2 is prime. Thus, S isn't empty.

  • Case 2: S = {x|x ∈ U and 2x is prime}

Let we take x from set U, then we have:

2x as multiple of 2 (ie even). All evens except 2 are non-prime. And we know that for 2x to be 2, we need x = 1 which isn't possible.

Thus, S can't get any value in it.
Thus, the set  {x|x ∈ U and 2x is prime} is null set, or empty set.

  • Case 3:  {x|x ∈ U and 1/2 x can be written as a fraction}

If we take x = 5, then (1/2)x = (5/2) which is a fraction. Thus, this set isn't empty, as we found 1 of its elements it will surely contain.

  • Case 4: {x|x ∈ U and 2x can be written as a fraction}

If we take x = 2, then 2x = 4 and 4 = 4/1 which is a fraction. Thus, this set isn't empty.

Thus,

Out of given sets the empty set is given as: Option B: {x|x ∈ U and 2x is prime}

Learn more about empty sets here:

https://brainly.com/question/4892299

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