MCQ_SINGLE
Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$. Then the number of elements in the relation $R = {((a_1, b_1), (a_2, b_2)) \in (A \times B, A \times B) : a_1$ divides $b_2$ and $a_2$ divides $b_1}$ is :
NUMERICAL
For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________
NUMERICAL
The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, 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: