Let $A = \{p, q, r\}$. Which of the following is an equivalence relation on $A$?

Let $A$ be a non-empty set of children in a family. The relation $R$ is defined on $A$ as '$x$ is a brother of $y$'. This relation is:

Let $R = \{(x, y) \in N \times N : \log_e(x + y) \leq 2\}$. Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is . . . . . . .

Show that the relation $R$ in the set $Z$ of integers given by $R = \{(a, b) : 2 \text{ divides } a - b\}$ is an equivalence relation.

Let a relation $R$ on $N \times N$ be defined as: $(x_1, y_1) R (x_2, y_2)$ if and only if $x_1 \leq x_2$ or $y_1 \leq y_2$. Consider the two statements:
$(I)$ $R$ is reflexive but not symmetric.
$(II)$ $R$ is transitive.
Then which one of the following is true?

The number of relations, defined on the set ${a, b, c, d}$, which are both reflexive and symmetric, is equal to: