The empty set has exactly one subset, which is itself: ∅.

The total number of subsets is 2^5 = 32.

The union of two sets includes all unique elements from both sets. Thus, I ∪ J = {1, 2, 3}.

The union of two sets includes all elements from both sets without duplicates. Thus, {1, 2} ∪ {2, 3} = {1, 2, 3}.

The union of two sets is the set of elements that are in either set. Here, {a, b} ∪ {b, c} = {a, b, c}.

cos^(-1)(0) corresponds to the angle where the cosine value is 0, which is π.

cot(cos^(-1)(1/2)) = √3

f(2) = 2^2 - 2(2) + 1 = 4 - 4 + 1 = 1.

The minimum value occurs at x = -b/(2a) = -2/(2k). Setting f(-1) = -3 gives k = -2.

sec^(-1)(2) = π/3, since sec(π/3) = 2.

sin(tan^(-1)(1)) = √2/2

sin(tan^(-1)(√3)) = √3/2

sin^(-1)(sin(π/4)) = π/4, as π/4 is in the range of sin^(-1).

tan^(-1)(√3) corresponds to the angle π/3.

By definition, \( \tan(\tan^{-1}(x)) = x \). Therefore, \( \tan(\tan^{-1}(3)) = 3 \).

An even function satisfies f(-x) = f(x). Here, f(x) = x^2 is even.

A function is even if f(-x) = f(x). Here, f(x) = x^2 is even.

h(x) = sqrt(x) is not a polynomial function.

g(x) = 1/x is not a polynomial because it has a negative exponent.

f(x) = 1/x is not continuous at x = 0.

The cosine function is periodic with a period of 2π.

A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.

A subset is a set that contains elements from another set. {1, 2} is a subset of {1, 2, 3}.

A subset can only contain elements that are in the original set. {x, y} is a valid subset of {x, y, z}.

An even function satisfies f(x) = f(-x). f(x) = x^2 is even.

The set {d} does not contain any elements from {a, b, c}, so it is not a subset.

The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).

The function f(x) = x^2 is non-negative for all real x, hence the range is all non-negative real numbers.

The minimum value of |x - 1| is 0 when x = 1, so the range is [0, ∞).

The relation x ~ y if x + y is even is reflexive, symmetric, and transitive, thus it is an equivalence relation.