Let's solve this step by step:

1. Power Set of $A$ (denoted as $P(A)$)

The Power Set of a set $A$ is the set of all possible subsets of $A$, including the empty set and $A$ itself.

Given $A = \{ 2, 3, 14, 21, 28 \}$, the power set $P(A)$ is:

$P(A) = \{ \emptyset, \{2\}, \{3\}, \{14\}, \{21\}, \{28\}, \{2, 3\}, \{2, 14\}, \{2, 21\}, \{2, 28\}, \{3, 14\}, \{3, 21\}, \{3, 28\}, \{14, 21\}, \{14, 28\}, \{21, 28\}, \{2, 3, 14\}, \{2, 3, 21\}, \{2, 3, 28\}, \{2, 14, 21\}, \{2, 14, 28\}, \{2, 21, 28\}, \{3, 14, 21\}, \{3, 14, 28\}, \{3, 21, 28\}, \{14, 21, 28\}, \{2, 3, 14, 21\}, \{2, 3, 14, 28\}, \{2, 3, 21, 28\}, \{2, 14, 21, 28\}, \{3, 14, 21, 28\}, \{2, 3, 14, 21, 28\} \}$

2. Arrow Diagram for the Relation $R$

The relation $R$ is defined on $A = \{ 2, 3, 14, 21, 28 \}$ as:

$R = \{(x, y) \in A \times A \mid x < y\}$

This means that we need to list pairs where $x$ is less than $y$ for elements in $A$.

The set of ordered pairs in $R$ is:

$R = \{ (2, 3), (2, 14), (2, 21), (2, 28), (3, 14), (3, 21), (3, 28), (14, 21), (14, 28), (21, 28) \}$

The arrow diagram visually shows these relations with arrows pointing from $x$ to $y$ for each pair where $x < y$. I can help describe the diagram:

1. Draw circles for each element in the set $A$: 2, 3, 14, 21, 28.
2. Draw arrows for each relation $(x, y)$, where the arrow points from $x$ to $y$.

Let me know if you'd like a sketch of this arrow diagram.

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Do you have any questions or want further details? Here are some related questions:

1. How do you calculate the number of elements in a power set?
2. What is the relationship between subsets and power sets?
3. Can you define different types of relations on a set?
4. What would the relation $R$ look like if $x \leq y$ instead of $x < y$?
5. How does an arrow diagram differ from other representations of relations?

Tip: The number of elements in a power set is $2^n$, where $n$ is the number of elements in the original set.