The number of relations on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$,which are reflexive and transitive but not symmetric,is

In a plane,two points $P$ and $Q$ are related if $OP = OQ$,where $O$ is a fixed point. The relation is:

Show that the relation $R$ in the set $A = \{x \in Z : 0 \leq x \leq 12\},$ given by $R = \{(a, b) : |a - b| \text{ is a multiple of } 4\},$ is an equivalence relation. Find the set of all elements related to $1$.

For the real numbers $x$ and $y$,we define the relation $p$ as $x p y$ if $x-y+\sqrt{2}$ is an irrational number. Then the relation $p$ is

Let $N$ be the set of natural numbers and the relation $R$ on $N \times N$ is defined by $(a, b) R (c, d)$ if $ad(b + c) = bc(a + d)$. Then $R$ is:

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$