Given,

S= {x:x≥ -2,x ∈ R}, which means $S$ contains all real numbers $x$ that are greater than or equal to -2.

Let's see from the option

a. [-2, ∞): This notation means the set includes all real numbers from -2 to infinity, including -2. This is correct because the set $S$ starts from -2 and includes all numbers greater than or equal to -2.

b. (-2, ∞): This notation means the set includes all real numbers greater than -2 but does not include -2 itself. This is not correct because the set S includes -2.

c. (∞, -2]: This notation is incorrect because it represents a set that includes all real numbers less than or equal to -2, which is the opposite of what is given.

d. [-2, ∞]: This notation means the set includes all real numbers from -2 to positive infinity, including both -2 and positive infinity. This is almost correct, but it should be ∞, not a closed interval.

Hence, the correct answer is option a. [-2, ∞)

Given,

S= {x:x≥ -2,x ∈ R}, which means $S$ contains all real numbers $x$ that are greater than or equal to -2.

Let's see from the option

a. [-2, ∞): This notation means the set includes all real numbers from -2 to infinity, including -2. This is correct because the set $S$ starts from -2 and includes all numbers greater than or equal to -2.

b. (-2, ∞): This notation means the set includes all real numbers greater than -2 but does not include -2 itself. This is not correct because the set S includes -2.

c. (∞, -2]: This notation is incorrect because it represents a set that includes all real numbers less than or equal to -2, which is the opposite of what is given.

d. [-2, ∞]: This notation means the set includes all real numbers from -2 to positive infinity, including both -2 and positive infinity. This is almost correct, but it should be ∞, not a closed interval.

Hence, the correct answer is option a. [-2, ∞)