document.write( "Question 1208962: Premise:
\n" ); document.write( "1.(∃x) (Ax • Bx) ∨ (∃x) (Cx ∨ Dx)
\n" ); document.write( "2.(∃x) (Ax ∨ Cx) ⊃ (x) Ex
\n" ); document.write( "3.~Em
\n" ); document.write( "Conclusion:
\n" ); document.write( "(∃x) Dx \n" ); document.write( "
Algebra.Com's Answer #848176 by textot(100)\"\" \"About 
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**1. (∃x) (Ax • Bx) ∨ (∃x) (Cx ∨ Dx)**
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\n" ); document.write( "\n" ); document.write( "**2. (∃x) (Ax ∨ Cx) ⊃ (x) Ex**
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\n" ); document.write( "\n" ); document.write( "**3. ~Em**
\n" ); document.write( " Given\r
\n" ); document.write( "\n" ); document.write( "**4. ~(x) Ex**
\n" ); document.write( " Universal Instantiation (3)\r
\n" ); document.write( "\n" ); document.write( "**5. ~[(∃x) (Ax ∨ Cx)]**
\n" ); document.write( " Modus Tollens (2, 4)\r
\n" ); document.write( "\n" ); document.write( "**6. ~[(∃x) (Ax ∨ Cx)] ≡ [~(∃x) Ax ∧ ~(∃x) Cx]**
\n" ); document.write( " De Morgan's Law (Quantifier Form)\r
\n" ); document.write( "\n" ); document.write( "**7. ~(∃x) Ax ∧ ~(∃x) Cx**
\n" ); document.write( " Equivalence (5, 6)\r
\n" ); document.write( "\n" ); document.write( "**8. ~(∃x) Ax**
\n" ); document.write( " Simplification (7)\r
\n" ); document.write( "\n" ); document.write( "**9. ~[(∃x) (Ax • Bx)]**
\n" ); document.write( " Simplification (7)\r
\n" ); document.write( "\n" ); document.write( "**10. ~(∃x) Ax ∨ ~[(∃x) Bx]**
\n" ); document.write( " De Morgan's Law (Quantifier Form) (9)\r
\n" ); document.write( "\n" ); document.write( "**11. ~(∃x) Ax**
\n" ); document.write( " Simplification (10)\r
\n" ); document.write( "\n" ); document.write( "**12. (∃x) (Cx ∨ Dx)**
\n" ); document.write( " Disjunctive Syllogism (1, 11)\r
\n" ); document.write( "\n" ); document.write( "**13. (∃x) Cx ∨ (∃x) Dx**
\n" ); document.write( " Distributive Law (Quantifier Form) (12)\r
\n" ); document.write( "\n" ); document.write( "**14. ~(∃x) Cx**
\n" ); document.write( " Simplification (7)\r
\n" ); document.write( "\n" ); document.write( "**15. (∃x) Dx**
\n" ); document.write( " Disjunctive Syllogism (13, 14)\r
\n" ); document.write( "\n" ); document.write( "**Therefore, (∃x) Dx**\r
\n" ); document.write( "\n" ); document.write( "This derivation demonstrates that the conclusion (∃x) Dx can be derived from the given premises using the specified rules of inference and quantifier negation.
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