If $A$ is the set of even natural numbers less than $8$ and $B$ is the set of prime numbers less than $7$, then the number of relations from $A$ to $B$ is
${2^9}$
${9^2}$
${3^2}$
${2^{9 - 1}}$
Let $R$ be the relation in the set $\{1,2,3,4\}$ given by $R =\{(1,2),\,(2,2),\,(1,1),\,(4,4)$ $(1,3),\,(3,3),\,(3,2)\}$. Choose the correct answer.
Show that each of the relation $R$ in the set $A=\{x \in Z: 0 \leq x \leq 12\},$ given by $R =\{( a , b ): a = b \}$ is an equivalence relation. Find the set of all elements related to $1$ in each case.
The relation $R= \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$ on set $A = \{1, 2, 3\}$ is
Let $S$ be the set of all real numbers. Then the relation $R = \{(a, b) : 1 + ab > 0\}$ on $S$ is
If $R$ is an equivalence relation on a set $A$, then ${R^{ - 1}}$ is