A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?

The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct?

1. It is possible to determine set A.

2. A × A contains the element (3, 2).

Select the correct answer using the code given below:

Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements is/are correct?

1. The domain of R is {1, 4, 7, 10, 13, 16).

2. The range of R is {1, 5, 9, 13, 17).

3. The range of R is equal to codomain of R.

Select the correct answer using the code given below:

Consider the following statements: 

1. The relation f defined by $f(x)= \begin{cases}x^3, & 0 \leq x \leq 2 \\ 4 x, & 2 \leq x \leq 8\end{cases}$ is a function.

2. The relation g defined by $g(x)= \begin{cases}x^2, & 0 \leq x \leq 4 \\ 3 x, & 4 \leq x \leq 8\end{cases}$ is a function.

Which of the statements given above is/are correct?