Given a relation **R** from **A={0, 1, 2, 3, 4}** to **B={0, 1, 2, 3}** as follows  **R={(a, b)| a>b}** then select all the ordered pairs such that **(a, b)∈ R**.

**Points will be deducted for each incorrect response; however, negative scoring will not be applied.**


Question 1 Select one or more:

(2, 4)


(0, 0)


(3, 2)


(2, 3)


(3, 4)


(1, 2)


(2, 1)


(4, 1)


(2, 2)


(0, 3)


(1, 4)


(4, 4)


(1, 3)


None of the listed answers is correct.


(4, 3)


(1, 0)


(2, 0)


(0, 4)


(3, 0)


(1, 1)


(4, 0)


(3, 3)


(0, 2)


(4, 2)


(3, 1)


(0, 1)

To determine which ordered pairs \((a, b)\) belong to the relation \(R = \{(a, b) \mid a > b\}\), we need to select pairs where the first element \(a\) is greater than the second element \(b\).

Let's analyze each of the provided pairs:

- \((2, 4)\): \(2 \not> 4\) (False)
- \((0, 0)\): \(0 \not> 0\) (False)
- \((3, 2)\): \(3 > 2\) (True)
- \((2, 3)\): \(2 \not> 3\) (False)
- \((3, 4)\): \(3 \not> 4\) (False)
- \((1, 2)\): \(1 \not> 2\) (False)
- \((2, 1)\): \(2 > 1\) (True)
- \((4, 1)\): \(4 > 1\) (True)
- \((2, 2)\): \(2 \not> 2\) (False)
- \((0, 3)\): \(0 \not> 3\) (False)
- \((1, 4)\): \(1 \not> 4\) (False)
- \((4, 4)\): \(4 \not> 4\) (False)
- \((1, 3)\): \(1 \not> 3\) (False)
- \((4, 3)\): \(4 > 3\) (True)
- \((1, 0)\): \(1 > 0\) (True)
- \((2, 0)\): \(2 > 0\) (True)
- \((0, 4)\): \(0 \not> 4\) (False)
- \((3, 0)\): \(3 > 0\) (True)
- \((1, 1)\): \(1 \not> 1\) (False)
- \((4, 0)\): \(4 > 0\) (True)
- \((3, 3)\): \(3 \not> 3\) (False)
- \((0, 2)\): \(0 \not> 2\) (False)
- \((4, 2)\): \(4 > 2\) (True)
- \((3, 1)\): \(3 > 1\) (True)
- \((0, 1)\): \(0 \not> 1\) (False)

So, the correct pairs that satisfy \(a > b\) are:
- \((3, 2)\)
- \((2, 1)\)
- \((4, 1)\)
- \((4, 3)\)
- \((1, 0)\)
- \((2, 0)\)
- \((3, 0)\)
- \((4, 0)\)
- \((4, 2)\)
- \((3, 1)\)

These are the correct options.

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Would you like further details or have any questions? Here are some related questions:

1. What is the formal definition of a relation in set theory?
2. Can a relation be defined with elements from only one set?
3. What is the difference between a relation and a function?
4. How can we determine if a relation is reflexive, symmetric, or transitive?
5. What are the possible relations from set \(A\) to set \(B\) in general?
6. Can a relation be represented using a matrix?
7. How does the concept of domain and range apply to relations?
8. What is an inverse relation, and how is it determined?

**Tip:** When dealing with relations, it's helpful to visually map out the elements of the sets to better understand the connections between them.

Learn how to determine which ordered pairs belong to a given relation R from set A to set B. This problem involves understanding the concept of relations and how to apply the condition (a > b) to select the correct pairs. Suitable for high school students studying set theory and relations.

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