The given problem involves a relation $R$ defined as a set of ordered pairs:

$R = \{(1,5), (4,5), (1,4), (4,6), (3,7), (7,6)\}$

You are asked to:

1. Find the domain of $R$,
2. Find the range (Jangkauan) of $R$,
3. Find the inverse of $R$.

1. Domain of $R$:

The domain of a relation is the set of all first elements (input values) from the ordered pairs. From the set of pairs $R$:

$R = \{(1,5), (4,5), (1,4), (4,6), (3,7), (7,6)\}$

The first elements are:

$\{1, 4, 1, 4, 3, 7\}$

After removing duplicates, the domain of $R$ is:

$\{1, 3, 4, 7\}$

2. Range of $R$:

The range is the set of all second elements (output values) from the ordered pairs. From the set $R$:

$R = \{(1,5), (4,5), (1,4), (4,6), (3,7), (7,6)\}$

The second elements are:

$\{5, 5, 4, 6, 7, 6\}$

After removing duplicates, the range of $R$ is:

$\{4, 5, 6, 7\}$

3. Inverse of $R$:

The inverse of a relation $R$, denoted $R^{-1}$, is obtained by swapping the elements in each ordered pair. For the relation $R = \{(1,5), (4,5), (1,4), (4,6), (3,7), (7,6)\}$, the inverse is:

$R^{-1} = \{(5,1), (5,4), (4,1), (6,4), (7,3), (6,7)\}$

Summary:

1. Domain of $R$: $\{1, 3, 4, 7\}$
2. Range of $R$: $\{4, 5, 6, 7\}$
3. Inverse of $R$: $\{(5,1), (5,4), (4,1), (6,4), (7,3), (6,7)\}$

Let me know if you want further details or have any questions.

Here are 5 related questions:

1. What is the codomain of a relation?
2. Can a relation be a function if its domain has repeated elements?
3. How do you graph a relation like $R$ on a Cartesian plane?
4. What is the significance of finding the inverse of a relation?
5. How is the composition of relations defined?

Tip: Inverse relations are useful in many mathematical contexts, such as solving equations or finding reverse processes in functions.