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?

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)

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)?

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.

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.)

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?

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