MCQ_SINGLE

Let $X = {1, 2, 3, 4, 5}$. The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X$, $Z \subseteq X$ and $Y \cap Z$ is empty, is:

NUMERICAL

The number of elements in the set $\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^{n}-3$ is a multiple of 7$\}$ is ___________.

MCQ_SINGLE

Let $R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)\}$ be a relation on the set $A = \{3, 6, 9, 12\}$. The relation is :

NUMERICAL

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

MCQ_SINGLE

Let a set $A = A_1 \cup A_2 \cup ..... \cup A_k$, where $A_i \cap A_j = \phi$ for $i \neq j$, $1 \le j, j \le k$. Define the relation R from A to A by $R = \{(x, y) : y \in A_i$ if and only if $x \in A_i, 1 \le i \le k\}$. Then, R is :

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