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}

The correct option is B.i.e., 2nd set.

Step-by-step explanation:

Given: U = {x : x is positive integer greater than 1}

               = {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,....}      

1st Set

say, X= {x : x∈U and is prime}

4∈U ⇒ ∈X as 2 is prime

∴This set is not empty set.

2nd Set

say, Y={x : x∈U and 2x is prime}

This set is empty set because product of 2 and no. greater than 1 is always a composite no.

3rd Set

say, Z={x : x∈U and can be written as fraction}

3∈U ⇒ ∈Z as is a fraction.

∴This set is not empty.

4th Set

say, S = {x : x∈U and 2x can be written as a fraction}

2∈U ⇒ 2.2 = 4 ∈S as this can be written as fraction or 3∈U ⇒ 2.3 = 6 ∈S as this can be written as fraction

∴This set is not empty.

Therefore, The correct option is B.

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