MCQ_SINGLE
If R is the smallest equivalence relation on the set ${1, 2, 3, 4}$ such that ${((1, 2), (1, 3))} \subset R$, then the number of elements in $R$ is __________.
NUMERICAL
Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$. Then the number of elements in the set $\{C \subseteq A: C \cap B \neq \phi\}$ is ___________.
NUMERICAL
Let $A=\{1,2,3, \ldots \ldots \ldots \ldots, 100\}$. Let $R$ be a relation on $\mathrm{A}$ defined by $(x, y) \in R$ if and only if $2 x=3 y$. Let $R_1$ be a symmetric relation on $A$ such that $R \subset R_1$ and the number of elements in $R_1$ is $\mathrm{n}$. Then, the minimum value of $\mathrm{n}$ is _________.
MCQ_SINGLE
Let R be a relation from the set ${1, 2, 3, …, 60}$ to itself such that $R = {(a, b) : b = pq}$, where $p, q \geqslant 3$ are prime numbers}. Then, the number of elements in R is :
NUMERICAL
Let $A=\{1,2,3,4,5,6,7\}$. Define $B=\{T \subseteq A$ : either $1 \notin T$ or $2 \in T\}$ and $C=\{T \subseteq A: T$ the sum of all the elements of $T$ is a prime number $\}$. Then the number of elements in the set $B \cup C$ is ________________.