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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}

Verified Answer :

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 \(\phi\) 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:

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