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The task in the image involves mathematical logic and asks to determine the truth value of a statement in the form of:

\[
\forall x \exists y (x + y = 3)
\]

Where \( x \) and \( y \) are real numbers.

### Step-by-step breakdown:

1. **Universal Quantifier (\( \forall x \))**: The statement claims that for **every** real number \( x \), there exists a real number \( y \) such that the equation \( x + y = 3 \) holds.

2. **Existential Quantifier (\( \exists y \))**: For each \( x \), we need to find at least one \( y \) such that the sum of \( x \) and \( y \) equals 3.

3. **Solving the equation**: The equation \( x + y = 3 \) can be rearranged to find \( y \):
   \[
   y = 3 - x
   \]
   For each real number \( x \), there is a corresponding \( y \) (namely \( y = 3 - x \)) that satisfies this equation.

### Conclusion:
Since for every real number \( x \), we can find a real number \( y = 3 - x \), the statement is **true**.

Would you like further details or explanations on any part of this? 

Here are 5 related questions you might find interesting:

1. What is the difference between universal and existential quantifiers in logic?
2. How do quantifiers change the truth value of logical statements?
3. Can you give an example of a false statement with quantifiers?
4. What are the applications of predicate logic in computer science?
5. How does mathematical logic relate to set theory?

**Tip**: When working with quantifiers, always check if the variable can satisfy the condition for all (universal quantifier) or at least one (existential quantifier) cases.

Determine the truth of the following statement for real numbers x and y: ∀x∃y(x + y = 3)

Explore the truth of the statement ∀x∃y(x + y = 3) using mathematical logic and quantifiers. This problem delves into the concept of universal and existential quantifiers in algebraic equations. Suitable for students in Grades 10-12.

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