Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Given

$ R_1 = \{(1,2),(5,3)\}\quad\quad R_2 = \{(6,4),(5,7)\}$

What is $R_2 \circ R_1$?

Because in my understanding, using the example

$ R_3 = \{(1,2),(3,4)\} \quad\quad R_4 = \{ (2,5),(6,7)\}$

Then $R_4\circ R_3 = \{(1,5)\}.\;$ Am I correct?

So given that case, if $R_2 \circ R_1 = (a,b),\;a$ comes from $R_1$, right? While $b$ comes from $R_2$?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

We have by definition (assembled from your example) \[ R_2 \circ R_1 = \{(a,b) \mid \exists c : (a,c) \in R_1, (c,b) \in R_2\} \] In the $R_4 \circ R_3$ example $(1,5) \in R_4 \circ R_3$ as we can "plug in" $2$ in the middle where $(1,2) \in R_3$, $(2,5) \in R_4$.

If there is no "matching" pair from $R_1$ and $R_2$ as it is in your case, there is no $(a,b)$ fulfilling the condition for being a member of $R_2 \circ R_1$, we have by definition $R_2 \circ R_1 = \emptyset$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.