The statement can be written in logical symbols as follows:

Let $x$ be a positive integer.

$x = 2 \ \lor \ \left( x \text{ is even} \land x > 2 \right) \ \lor \ \left( x \text{ is odd} \land x \text{ is prime} \right) \ \lor \ \left( x \text{ is odd} \land x \text{ is composite} \right)$

Breaking down each condition:

• $x = 2$
• $\left( x \text{ is even} \land x > 2 \right)$ can be expressed as $\left( x \mod 2 = 0 \land x > 2 \right)$
• $\left( x \text{ is odd} \land x \text{ is prime} \right)$ can be expressed as $\left( x \mod 2 \neq 0 \land \text{Prime}(x) \right)$
• $\left( x \text{ is odd} \land x \text{ is composite} \right)$ can be expressed as $\left( x \mod 2 \neq 0 \land \neg \text{Prime}(x) \land x > 1 \right)$

Thus, the full logical expression is:

$x = 2 \ \lor \ \left( x \mod 2 = 0 \land x > 2 \right) \ \lor \ \left( x \mod 2 \neq 0 \land \text{Prime}(x) \right) \ \lor \ \left( x \mod 2 \neq 0 \land \neg \text{Prime}(x) \land x > 1 \right)$

Would you like any further details or clarification?

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Here are 5 related questions you might explore:

1. What is the logical symbol for "if and only if" and how does it apply to this statement?
2. How would you express the condition for $x$ being a prime number using logical symbols?
3. Can a number be both even and odd? How would that be expressed in logic?
4. How does modular arithmetic help in determining whether a number is even or odd?
5. What are the logical conditions for a number being composite?

Tip: Using modular arithmetic (like $x \mod 2 = 0$) is a simple way to check if a number is even or odd in logic.