MCQ_SINGLE

Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$. Let $R$ be a relation defined on $A \times B$ such that $R = {((a_1, b_1), (a_2, b_2)): a_1 \le b_2 \text{ and } b_1 \le a_2}$. Then the number of elements in the set R is :

MCQ_SINGLE

The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :

NUMERICAL

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

MCQ_SINGLE

Let $R = \{(1, 2), (2, 3), (3, 3)\}$ be a relation defined on the set $\{1, 2, 3, 4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, 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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