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.