Find relation from given task

Question

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.

score 1 · Accepted Answer · answered Oct 04 '17 at 20:07

1

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.

answered Oct 04 '17 at 20:07

Austin Weaver

2,059

Please post final result also – IntoTheDeep Oct 05 '17 at 06:13
Still not clear to me – IntoTheDeep Oct 05 '17 at 06:14
${(1,1),(2,3),(2,4),(3,3),(3,4),(4,1)}$ Is that correct? – IntoTheDeep Oct 05 '17 at 06:50
$R_2;R_1 = {(1,2),(1,3),(1,4),(3,2),(3,3),(4,4),(4,3)}$ correct? – IntoTheDeep Oct 05 '17 at 07:00
1

Those are correct. – Austin Weaver Oct 05 '17 at 14:38

Find relation from given task

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