If R is a relation on $A = \{a, b, c\}$ such that $R = \{(a,a), (b,b)\}$, which element/elements should be included to make R an equivalence relation.

A. (c, c)

B. (c, c), (a, c), (c, a)

C. (a, b), (b, c), (a, c)

D. (b, c), (c, c), (c, a), (b, a)

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A and B are two sets such that $n(A) = 5$ and $n(B) = 7$. The number of one-one functions from A to B is

The number of equivalence relation on the set $\{1, 2, 3\}$ containing $(1, 2)$ and $(2, 1)$ is

The greatest integer function $f: R\to R$ defined by $f(x) = [x]$, then which of the following are true?

(A) $f(x)$ is one - one and onto.

(B) Domain of $f(x) = R$ (the set of real numbers).

(C) $f(x)$ is neither one-one nor onto.

(D) Range of $f(x) = Z$ (The set of integers).

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The relation R in $\mathbb{R}$ (set of real numbers) is defined by $R = \{(a,b): a \leq b^3\}$, then R is

Let L be the set of all lines in a plane and R be the relation on set L defined by $R = \{(L_1, L_2): L_1 \perp L_2\}$ Then R is

(A) an equivalence Relation

(B) a symmetric Relation

(C) not a transitive Relation

(D) a reflexive Relation

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Let $A$ be set of all real numbers and $R$ be a relation on $A$ defined by $R=\{(a,b): 1+ab>0\}$, then relation $R$ is