In the set $A = \{1, 2, 3, 4, 5\}$,a relation $R$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is

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

Let $r$ be a relation on the set $N \times N$ defined by $(a, b)r(c, d) \Rightarrow a + d = b + c$. Then $r$ is:

For $\alpha \in N$,consider a relation $R$ on $N$ given by $R = \{(x, y) : 3x + \alpha y \text{ is a multiple of } 7\}$. The relation $R$ is an equivalence relation if and only if:

Let $P$ be the relation defined on the set of all real numbers such that $P = \{(a,b) : \sec^2 a - \tan^2 b = 1\}$. Then $P$ is

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