# Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find

• Oct 28th 2013, 03:54 PM
lamentofking
Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2),(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find

b) R1 ∩ R2.
c) R1 − R2.

So with b). Does this mean the ordered pairs in R1 and R2?
And with c) does this mean the sets in R1 that are not in R2?

What does the part of the problem, " be relations
from {1, 2, 3} to {1, 2, 3, 4}" mean?
• Oct 28th 2013, 04:50 PM
Plato
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
Quote:

Originally Posted by lamentofking
What does the part of the problem, " be relations
from {1, 2, 3} to {1, 2, 3, 4}" mean?

Any subset of $\displaystyle A\times B$ is a relation $\displaystyle A\to B$. (some authors do not allow the empty relation)
• Nov 2nd 2013, 05:30 AM
lamentofking
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
So for b) R1 ∩ R2. The answer is all the ordered pairs in R1 (Since they are in R2)?
• Nov 2nd 2013, 07:11 AM
HallsofIvy
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
Quote:

Originally Posted by lamentofking
Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2),(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find

b) R1 ∩ R2.
c) R1 − R2.

So with b). Does this mean the ordered pairs in R1 and R2?

Yes.

Quote:

And with c) does this mean the sets in R1 that are not in R2?
Well, "ordered pairs", not "sets" but yes.

Quote:

What does the part of the problem, " be relations
from {1, 2, 3} to {1, 2, 3, 4}" mean?
A "relation from set A to set B" is a set of ordered pairs in which the first member of each pair is in A and the second member is in B.
So, here, "relations from {1, 2, 3} to {1, 2, 3, 4}" are sets of ordered pair where the first member of each pair one of 1, 2, or 3 and the second member is one of 1, 2, 3, or 4. You should see that this is true for the given relations.
• Nov 2nd 2013, 07:14 AM
HallsofIvy
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
Quote:

Originally Posted by lamentofking
So for b) R1 ∩ R2. The answer is all the ordered pairs in R1 (Since they are in R2)?

Yes, $\displaystyle R1\cap R2= R1$. And because, as you say, $\displaystyle R1\subset R2$, $\displaystyle R1- R2$ is just as easy. (I think Plato's parenthetical statement must not apply here.)
• Nov 2nd 2013, 08:26 AM
lamentofking
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
So then because R1 and R2 share the same ordered pairs, R1 - R2 is equal to the empty set correct?
• Nov 2nd 2013, 10:16 AM
HallsofIvy
Re: Let R1 and R2 be relations from {1, 2, 3} to {1, 2, 3, 4}. Find
Yes.