Question

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

Which is an empty set?

{x|x ∈ U andOne-half is prime}
{x|x ∈ U and 2x is prime}
{x|x ∈ U andOne-half can be written as a fraction}
{x|x ∈ U and 2x can be written as a fraction}

Answer 1

Answer:

It's B

Step-by-step explanation:

I just took the test and got it right. :D

Answer 2

Using the definition of an empty set, we can see that the empty set in the options is:

{x|x ∈ U and 2x is prime}

Which is an empty set?

First, we know that:

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

So we can write:

U = {2, 3, ...}

Now, take in mind that if:

x ∈ U

Then x is a natural number larger than 1.

Now, if we multiply a natural number different than 1 by 2, we get:

2x

because x is a natural number larger than 1, 2x can't be a prime number (because it is divisible by 2 and by x).

Then the set that is empty is:

{x|x ∈ U and 2x is prime}

Because there is no element x in U that meets the condition that 2x must be prime.

If you want to learn more about empty sets:

https://brainly.com/question/14691345

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