A relation R on the set $A = \{1, 2, 3, \ldots, 13, 14\}$ defined as $R = \{(x,y): 3x - y = 0\}$ is

If $A = \{1, 2, 3, 4, ..., n\}$ and $B = \{x, y\}$, then the number of surjections from A to B is

The relation R in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (1, 3), (2, 3)\}$ is:

For the functions $f(x) = x^2$ and $g(x) = x^3$, which of the following statements are TRUE?

[where N is the set of natural numbers and Z is the set of integers]

(A) $f: N \to N$ is one-one but not onto.

(B) $f: Z \to Z$ is neither one-one nor onto.

(C) $g: N \to N$ is one-one but not onto.

(D) $g: Z \to Z$ is one-one but not onto.

Choose the correct answer from the options given below:

Relation R on Real Numbers is defined as $R = \{(a, b) : a \leq b\}$. The relation is :

If $R$ is a relation on $Z$ (set of all integers) defined by $xRy$, iff $|x - y| \leq 1$, then

(a) $R$ is reflexive

(b) $R$ is symmetric

(c) $R$ is transitive

(d) $R$ is not symmetric

(e) $R$ is not transitive

Choose the most appropriate answer from the options given below

If a relation R is defined on the set $X = \{1, 2, 3, 4\}$ as $R = \{(1,1), (2,2), (3,4), (4,3)\}$, then R is