Is following Relation from $X$ to $Y$ is a Relation or not?

Question

$$X=\{1,2,3,4,5\} \text{ and } Y=\{1,3,5,7,9\}$$

$$R=\{(x,y)\mid y=2+x,x\in X, y\in Y\}$$

my textbook says it is a relation from $X$ to $Y$. But for $x=2$, $y=4$ but $4$ is not in $Y$. How is that possible?

Sounds like a typo; perhaps they intended a relation of $y = 2x - 1$. — Daniel R. Collins, Apr 05 '16 at 18:37

score 1 · Answer 1 · answered Apr 05 '16 at 18:38

1

Any relation between $X$ and $Y$ is a subset of $X\times Y$, so $R$ qualifies.

By the way, use $\in$ instead of $\epsilon$.

answered Apr 05 '16 at 18:38

Henricus V.

R is not subset of X \times Y...so its clear it is typo – T.Noor Apr 05 '16 at 18:46
@T. Noor It says that $x\in X, y\in Y$ – Henricus V. Apr 05 '16 at 18:46
sir, there is (2,4) in R which is not in X\times Y – T.Noor Apr 05 '16 at 18:49
@I'm interpreting $,$ as $\land$, but it depends on the context. – Henricus V. Apr 05 '16 at 18:50

1 Answers1