Question 1208962
**1. (∃x) (Ax • Bx) ∨ (∃x) (Cx ∨ Dx)**
    Given

**2. (∃x) (Ax ∨ Cx) ⊃ (x) Ex**
    Given

**3. ~Em**
    Given

**4. ~(x) Ex**
    Universal Instantiation (3)

**5. ~[(∃x) (Ax ∨ Cx)]**
    Modus Tollens (2, 4)

**6. ~[(∃x) (Ax ∨ Cx)] ≡ [~(∃x) Ax ∧ ~(∃x) Cx]**
    De Morgan's Law (Quantifier Form)

**7. ~(∃x) Ax ∧ ~(∃x) Cx**
    Equivalence (5, 6)

**8. ~(∃x) Ax**
    Simplification (7)

**9. ~[(∃x) (Ax • Bx)]**
    Simplification (7)

**10. ~(∃x) Ax ∨ ~[(∃x) Bx]**
    De Morgan's Law (Quantifier Form) (9)

**11. ~(∃x) Ax**
    Simplification (10)

**12. (∃x) (Cx ∨ Dx)**
    Disjunctive Syllogism (1, 11)

**13. (∃x) Cx ∨ (∃x) Dx**
    Distributive Law (Quantifier Form) (12)

**14. ~(∃x) Cx**
    Simplification (7)

**15. (∃x) Dx**
    Disjunctive Syllogism (13, 14)

**Therefore, (∃x) Dx**

This derivation demonstrates that the conclusion (∃x) Dx can be derived from the given premises using the specified rules of inference and quantifier negation.