Here are the English statements rewritten in symbolic form using quantifiers:

1. Birds of the same feather, flock together.

   • $\forall x \forall y (F(x) \land F(y) \Rightarrow Flock(x, y))$
   • Where $F(x)$ means "x is a bird of the same feather" and $Flock(x, y)$ means "x and y flock together."

2. Cheaters never win.

   • $\forall x (Cheater(x) \Rightarrow \neg Win(x))$
   • Where $Cheater(x)$ means "x is a cheater" and $Win(x)$ means "x wins."

3. All real numbers are complex numbers.

   • $\forall x (Real(x) \Rightarrow Complex(x))$
   • Where $Real(x)$ means "x is a real number" and $Complex(x)$ means "x is a complex number."

4. All fractions are rational numbers.

   • $\forall x (Fraction(x) \Rightarrow Rational(x))$
   • Where $Fraction(x)$ means "x is a fraction" and $Rational(x)$ means "x is a rational number."

5. All odd numbers are prime numbers.

   • $\forall x (Odd(x) \Rightarrow Prime(x))$
   • Where $Odd(x)$ means "x is an odd number" and $Prime(x)$ means "x is a prime number."

6. Some even numbers are prime numbers.

   • $\exists x (Even(x) \land Prime(x))$
   • Where $Even(x)$ means "x is an even number" and $Prime(x)$ means "x is a prime number."

7. The empty set is a subset of all sets.

   • $\forall A (\emptyset \subseteq A)$
   • Where $\emptyset$ denotes the empty set and $A$ represents any set.

8. Even numbers are divisible by two.

   • $\forall x (Even(x) \Rightarrow \exists k (x = 2k))$
   • Where $Even(x)$ means "x is an even number" and $x = 2k$ means "x is divisible by 2."

9. For all composite numbers, there exists some even numbers, which are divisible by 4.

   • $\forall x (Composite(x) \Rightarrow \exists y (Even(y) \land y \text{ is divisible by } 4))$
   • Where $Composite(x)$ means "x is a composite number" and $Even(y)$ means "y is an even number."

10. For all composite numbers, there exists some odd numbers, which are divisible by 10.

    • $\forall x (Composite(x) \Rightarrow \exists y (Odd(y) \land y \text{ is divisible by } 10))$
    • Where $Composite(x)$ means "x is a composite number" and $Odd(y)$ means "y is an odd number."

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Would you like further clarification on any of these? Here are some related questions to help you dive deeper into quantifiers:

1. How can you use quantifiers to express "At least one person is happy"?
2. What does it mean for a set to be a subset of another set in symbolic logic?
3. How does the negation of a quantifier affect its meaning in logic?
4. How do universal and existential quantifiers differ in logical expressions?
5. Can you write a statement involving both existential and universal quantifiers in mathematics?

Tip: When writing symbolic logic, it's helpful to clearly define what each symbol and variable represents before applying quantifiers.