Solution:
First, let's examine each option to determine which of them is a singleton set. A singleton set is a set that contains exactly one element.
Option A:
{x:x2=4,x∈ℝ}
This set includes all real numbers x for which x2=4, which means x could be either 2 or -2 because both satisfy the equation. Thus, this set contains more than one element ( 2 and -2 ) and is not a singleton set.
Option B:
{x:|x|<4,x∈ℕ}
In this set, x must be a natural number, and |x| must be less than 4 . This condition is satisfied for x=1,2,3, as these are the natural numbers less than 4 . With multiple elements (1,2,3), this is not a singleton set either.
Option C:
{x:|x|<−4,x∈ℕ}
This set is looking for natural numbers that satisfy the expression |x|<−4. Since the absolute value of any real number (including natural numbers) is always non-negative, there is no value of x for which |x|<−4. As a result, this set is empty, known as the empty set, and is therefore also not a singleton set.
Option D:
{x:x2=4,x∈ℕ}
This set contains natural numbers x that satisfy x2=4. In the set of natural numbers, the only number that satisfies this condition is 2 , as -2 is not a natural number. Hence, this set contains exactly one element (2).
From the analysis above, Option D is the correct choice as it is a singleton set, containing exactly one element, 2.
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