Answer to Question #179437 in Discrete Mathematics for Rameen

Question

 Let A = {2,4} and B = {6,8,10} and define relations R and S from A to B as follows: For all (x, y) E A ® B, XRy iff x|y, and xSy iff y - 4 = x. State explicitly which ordered pairs are in A x B, R, S, RUS, and RNS

Answer 1

Let $A = \{2,4\}$ and $B = \{6,8,10\}$ and define relations $R$ and $S$ from $A$ to $B$ as follows:

For all $(x, y) \in A \times B$, $xRy$ iff $x|y$, and $xSy$ iff $y - 4 = x$.

Let us state explicitly which ordered pairs are in $A \times B, R, S, R\cup S,$ and $R\cap S$:

$A\times B=\{(2,6),(2,8),(2,10),(4,6),(4,8),(4,10)\}$

$R=\{(2,6),(2,8),(2,10),(4,8)\}$

$S=\{(2,6),(4,8)\}$

$R\cup S=\{(2,6),(2,8),(2,10),(4,8)\}$

$R\cap S=\{(2,6),(4,8)\}$