Let $R$ be a relation on a set $A$ such that $R = R^{-1}$. Then $R$ is:

Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Choose the correct answer.

Let $\rho$ be a relation defined on $N$, the set of natural numbers, as $\rho = \{(x, y) \in N \times N : 2x + y = 41\}$. Then:

For a set $A = \{1, 2, 3\}$,a relation $R = \{(1, 2), (2, 3)\}$ is defined. What is the minimum number of ordered pairs that must be added to $R$ to make it an equivalence relation?

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

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 2), (2, 1)\}$ is symmetric but neither reflexive nor transitive.