Relations and Functions

Which of the following properties does the relation $R = \{(1, 2), (2, 1), (1, 1), (2, 2)\}$ on the set $A = \{1, 2, 3\}$ NOT possess?

Let $A$ be the set of all people in a town. The relation $R = \{(x, y) : x \text{ is a friend of } y\}$ (assuming friendship is mutual and everyone is their own friend) is:

On the set $\mathbb{R}$ of real numbers, the relation $R$ defined by $aRb \iff a^2 + b^2 = 4$ is:

Let $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$. A function $f: A \to B$ defined by $f(x) = x + 1$ is:

The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \sqrt[3]{x}$ is:

The function $f: [0, \infty) \to [0, 1)$ defined by $f(x) = \frac{x}{x+1}$ is: