GO Classes Set Theory And Algebra Practice Set 1 | Question: 3

Question

The following table describes a binary relation. Find the set of ordered pairs that is this relation, as in the definition of a binary relation.
$$
\begin{array}{c|c|c|c|c|c|c|}
\sim & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline 1 &  \ast  & & & & &  \ast  \\
\hline 2 & &  \ast  & & & & \\
\hline 3 & & & &  \ast  &  \ast  & \\
\hline 4 & & &  \ast  & &  \ast  & \\
\hline 5 & & &  \ast  &  \ast  & & \\
\hline 6 &  \ast  & & & & &  \ast  \\
\hline
\end{array}$$

Answer 1

Ordered pairs of this relation :- (1,1),(1,6),(2,2),(3,4),(3,5),(4,3),(4,5),(5,3),(5,4),(6,1),(6,6).

total ordered pairs = 11

Answer 2

The ordered pair of the given relation is as follows:

$R= \left\{ (1,1)\ (1,6)\ (2,2)\ (3,4)\ (3,5)\ (4,3)\ (4,5) \ (5,3)\ (5,4)\ (6,1)\ (6,6)\right \}$