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.

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.