If 'a' is included, we can choose from the remaining elements {b, c}. The subsets containing 'a' are {a}, {a, b}, {a, c}, and {a, b, c}, totaling 4 subsets.

The union of two sets includes all unique elements from both sets. Here, the union is {a, b, c, d}.

The power set of a set with n elements has 2^n subsets. For E, n = 2, so the size of the power set is 2^2 = 4.

The prime numbers less than 10 are 2, 3, 5, and 7. Therefore, E = {2, 3, 5, 7}.

The prime numbers less than 10 are {2, 3, 5, 7}. The power set has 2^4 = 16 elements.

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

The total number of subsets of a set with n elements is 2^n. For F, n = 4, so there are 2^4 = 16 subsets. Proper subsets are total subsets minus the set itself, so 16 - 1 = 15.

The power set of a set with n elements has 2^n elements. For F, n = 3, so the power set has 2^3 = 8 elements.

The subsets containing exactly 2 elements are {a, b}, {a, c}, and {b, c}. So, there are 3 such subsets.

The even numbers between 1 and 10 are 2, 4, 6, and 8. Therefore, F = {2, 4, 6, 8}.

The size of the power set is 2^n where n is the number of elements in the set. Here, n = 3, so the size is 2^3 = 8.

The subsets of F that do not contain 'y' are {∅, {x}}, totaling 2 subsets.

Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.

f(5) = 2(5) + 3 = 10 + 3 = 13.

f(2) = 2(2^2) - 3(2) + 1 = 8 - 6 + 1 = 3.

f(3) = 2^3 = 8.

f(-2) = 3(-2) - 4 = -6 - 4 = -10.

f(-2) = 3(-2) - 4 = -6 - 4 = -10.

To find the inverse, set y = 3x - 4, solve for x: x = (y + 4)/3, thus f^(-1)(x) = (x + 4)/3.

First, find f(1) = 3(1) - 5 = -2. Then, f(-2) = 3(-2) - 5 = -6 - 5 = -11.

f(π/2) = sin(π/2) = 1.

The vertex form is f(x) = (x + 1)^2, so the vertex is (-1, 0).

To find x-intercepts, set f(x) = 0: x^2 - 4 = 0, which gives x = ±2.

f(2) = 2^2 - 4*2 + 3 = 4 - 8 + 3 = -1.

(f ∘ g)(2) = f(g(2)) = f(2 + 1) = f(3) = 3^2 = 9.

f(-3) = (-3)^2 = 9.

f(1) = 1^3 - 3(1) + 2 = 1 - 3 + 2 = 0.

f(1) = 1^3 - 3(1) + 2 = 1 - 3 + 2 = 0.

f(2) = |2 - 2| = |0| = 0.

f(-3) = |-3| = 3.