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The image you uploaded contains a mathematical question in Portuguese regarding sets and relations. The problem defines two sets of ordered pairs, \( r \) and \( s \), and then lists four assertions to be verified. Here's a translation of the question for clarity:

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**Let the relations** \( r = \{ (1, 2), (3, 4), (5, 6) \} \) **and** \( s = \{ (1, 2), (4, 5) \} \). **Considering the definition of operations between relations, we have the following statements:**

I. \( 4r^c s \ 5 \).

II. \( 2(r - s) 1 \).

III. \( (r \cap s)^{-1} = 2 \).

IV. \( 3(r \circ s)4 \).

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Let me clarify or solve these:

1. **Intersection and Complement:** 
   - \( r^c s \) refers to the complement of \( r \) relative to \( s \), which generally involves elements not in the intersection of \( r \) and \( s \).
  
2. **Set Difference \( r - s \):**
   - This operation finds pairs in \( r \) that are not in \( s \).

3. **Inverse Relation \( (r \cap s)^{-1} \):**
   - This checks for the inverse of the intersection of relations \( r \) and \( s \).

4. **Composition of Relations \( r \circ s \):**
   - Composition of relations deals with chaining pairs based on the second element of the first set and the first element of the second set.

Let me know if you'd like detailed verification for each statement.

Sejam as relações r = {(1, 2), (3, 4), (5, 6)} e s = {(1, 2), (4, 5)}, considerando a definição das operações entre relações, temos as seguintes afirmações: I. 4(r^c s)5. II. 2(r - s)1. III. (r ∩ s)^-1 = 2. IV. 3(r ∘ s)4.

Explore a mathematical problem involving operations on relations, including set intersection, difference, inverse, and composition. Understand how to apply these operations in set theory using example relations r = {(1, 2), (3, 4), (5, 6)} and s = {(1, 2), (4, 5)}.

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