Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation on the set $A \times A$ defined by $R = \{((a, b), (c, d)) : 2a + 3b = 4c + 5d\}$. Then the number of elements in $R$ 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:

Determine whether the following relation is reflexive,symmetric,and transitive:
Relation $R$ in the set $A$ of human beings in a town at a particular time given by:
$R = \{(x, y) : x \text{ is exactly } 7 \, cm \text{ taller than } y\}$

Let $R$ be a reflexive relation on a finite set $A$ containing $n$ elements,and let $R$ contain $m$ ordered pairs. Then,

The maximum number of equivalence relations on the set $A = \{1, 2, 3, 4\}$ is $N$. Then -

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