Which of the following is a null set:

• A {0}
• B {x: x > 0 or x < 0}
• C {x: x² = 4 or x = 3}
• D {x: x² + 1 = 0, x ∈ R}

To identify the null set among the options provided, let's analyze each one:

Option A: {0}

This set contains one element, which is 0. Therefore, it is not a null set.

Option B: {x: x > 0}

This set includes all positive numbers. It is not empty, so it is not a null set.

Option C: {x: x² = 4 or x = 3}

This set includes the numbers 2, -2, and 3, since these values satisfy the equation. Thus, it is not a null set.

Option D: {x: x² + 1 = 0, x ∈ R}

This equation has no real solutions because the square of any real number is non-negative, making the expression always greater than zero. Therefore, this set is empty.

Final Answer

The null set among the options is Option D: {x: x² + 1 = 0, x ∈ R}.