$A$ relation $R$ defined on a set $A$ is anti-symmetric if $(a, b) \in R$ and $(b, a) \in R$ implies:

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$. Find the domain of $R$.

On the set $R$ of real numbers,the relation $\rho$ is defined by $x \rho y$ if $x > |y|$. Which of the following statements is true regarding the properties of $\rho$?

The relation $R$ is defined on the set $N$ by $R = \{(x, y) | x, y \in N, 2x + y = 41\}$. Then $R$ is:

On the power set $P(A)$ of a set $A$,the relation "is a subset of" $(\subseteq)$ is:

In the set of all $3 \times 3$ real matrices,a relation is defined as follows: $A$ matrix $A$ is related to a matrix $B$ if and only if there exists a non-singular $3 \times 3$ matrix $P$ such that $B = P^{-1} A P$. This relation is