Given set A={2, 3, 14,21,28}.
1. Write the power set of A, P(A).
2. Draw an arrow diagram for the relation R defined on the set A such that R={(x,y), x<у}

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.

Given set A = {2, 3, 14, 21, 28}, 1. Write the power set of A, P(A). 2. Draw an arrow diagram for the relation R defined on the set A such that R = {(x, y) | x < y}.

Explore how to determine the power set of A = {2, 3, 14, 21, 28}, which includes all possible subsets of the set. Also, learn to draw an arrow diagram representing the relation R = {(x, y) | x < y} on the set A. This problem is suitable for students in Grades 9-11.

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