Question B1:

Question B2:

Question B3:

Question B4:

Question B5:

Let $A_1, A_2, A_3,$ and $A_4$ be the equivalence classes of $R$ with sizes $3, 5, 3,$ and $2,$.

Then the ordered pairs $(a,b)$ such that $a$ and $b$ are in the same equivalence class. For any $i\in\{1,2,3,4\}$, there are ${|A_i|\choose 2} = \frac{|A_i|(|A_i|-1)}{2}$ ordered pairs of elements in $A_i$. Therefore, the total number of ordered pairs in $R$ is:

$$ {∣A1∣\choose 2}+{∣A2∣\choose 2}+{∣A3∣\choose2}+{∣A4∣\choose2}\\=3⋅2/2+5⋅4/2+3⋅2/2+2⋅1/2=22 $$

So there are $22$ ordered pairs in $R$.