My target is to find relation from given task. Please include explanations of solving not just an answer. Thank you. $$A = \{ 1, 2, 3, 4 \} $$ $$R_1 = \{ (1, 2), (1, 3), (2, 4), (2, 2), (3, 4), (4, 3) \}$$ $$R_2 = \{ (1,1), (1,2), (3,1), (4,3), (4, 4) \}$$ How to find $R_1;R_2$ and $R_2;R_1$?
I have no idea from where to start. What must be my first step? Please help me to find logic between this.
For the first composition:
For each $a\in A$, find all elements $b\in A$ such that $a R_1 b$.
In this problem, for $a=1$, $b=2,3$.
Now, for each possible value of $b$, add all $(a,c)$ such that $bR_2c$ to your new relation.
The relation so far is then $\{ (1,1) \}$, because $2$ relates to nothing in $R_2$ and $3$ relates only to $1$ in $R_2$.
Repeating this process for all $a$ yields the composition of the two relations.