NUMERICAL
Let $A=\{1,2,3, \ldots, 20\}$. Let $R_1$ and $R_2$ two relation on $A$ such that $R_1=\{(a, b): b$ is divisible by $a\}$ $R_2=\{(a, b): a$ is an integral multiple of $b\}$. Then, number of elements in $R_1-R_2$ is equal to _____________.
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 ________
MCQ_SINGLE
Let $A = \{1, 2, 3, 4, 5, 6, 7\}$. Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ is :
MCQ_SINGLE
Consider the following two binary relations on the set $A = {a, b, c}$:
$R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)}$ and
$R_2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$.
Then: