R is symmetric because if (x,y) is in R, then (y,x) is also in R. It is not reflexive or transitive.

cos^(-1)(0) = π, since cos(π) = 0.

sin^(-1)(sin(π/4)) = π/4

If sin(x) = 1/√2, then x = π/4, thus tan(sin^(-1)(1/√2)) = tan(π/4) = 1.

tan^(-1)(√3) = π/3, since tan(π/3) = √3.

sin^(-1)(x) + cos^(-1)(x) = π/2 for all x in the domain [-1, 1].

Using the identity sin^(-1)(x) + sin^(-1)(√(1-x^2)) = π/2 for x in [0, 1], the value is π/2.

2sin^(-1)(1/2) = 2(π/6) = π/3 and 2cos^(-1)(1/2) = 2(π/3) = 2π/3. Therefore, the total is π/3 + 2π/3 = π.

By definition, \( \cos(\cos^{-1}(x)) = x \). Therefore, \( \cos(\cos^{-1}(\frac{3}{5})) = \frac{3}{5} \).

Using the identity, cos(tan^(-1)(3/4)) = 4/5

cos^(-1)(0) = π/2, since cos(π/2) = 0.

sin^(-1)(√3/2) = π/3 and cos^(-1)(1/2) = π/3. Therefore, the sum is π/3 + π/3 = 2π/3.

By definition, \( \sin(\sin^{-1}(x)) = x \). Therefore, \( \sin(\sin^{-1}(\frac{1}{2})) = \frac{1}{2} \).

If 1 is included, we can choose from the remaining elements {2, 3, 4}, which has 2^3 = 8 subsets.

The number of ways to choose 2 elements from 4 is given by the combination formula C(4,2) = 6.

The subsets with exactly 2 elements are {a, b}, {a, c}, and {b, c}. Total = 3.

The power set of the empty set contains only one subset, which is the empty set itself. Thus, it has 1 element.

The number of relations on a set with n elements is 2^(n^2). For n = 3, it is 2^(3^2) = 2^9 = 512.

The number of subsets of a set with n elements is 2^n. Here, n = 4, so 2^4 = 16.

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

The number of subsets of a set with n elements is 2^n. Here, n = 6, so 2^6 = 64.

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.

The number of subsets of a set with n elements is given by 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

The number of subsets of a set with n elements is 2^n. Here, n=4, so the number of subsets is 2^4 = 16.

The only subset that does not contain y is {∅} and {x}. Total = 2.

A is a subset of B if all elements of A are in B. Here, all elements of A are in B, so A ⊆ B is true.

A ∪ B = {1, 2, 3, 4}, which has 4 elements. The number of subsets is 2^4 = 16.

The number of elements in the Cartesian product A × B is the product of the number of elements in A and B. Here, |A| = 3 and |B| = 2, so |A × B| = 3 * 2 = 6.

The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.