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Logic Practice Problems

Solution for Problems October 12
1. (x)[(Px v Qx) ⊃ (Rx • Sx)]		/(∃x)(Px v Sx) ⊃ (∃x)Sx
	2. (∃x)(Px v Sx)		ACP
	3. Pa v Sa			2, EI
	4. (Pa v Qa) ⊃ (Ra • Sa)		1, UI
		5. ~Sa			AIP
		6. Sa v Pa		3, Com
		7. Pa			5+6, DS
		8. Pa v Qa		7, Add
		9. Ra • Sa		4+8, MP
		10. Sa • Ra		9, Com
		11. Sa			10, Simp
		12. Sa • ~Sa		5+11, Conj
	13. ~~Sa			5-12, IP
	14. Sa				13, DN
	15. (∃x)Sx			14, EG
16. (∃x)(Px v Sx) ⊃ (∃x)Sx		2-15, CP

The novel on the table was written by Margaret Mitchell.
The only novel Margaret Mitchell wrote is Gone with the Wind.
Therefore, the novel on the table is Gone with the Wind.
(Nx: x is a novel; Tx: x is on the table; Wxy: x wrote y;
m: Margaret Mitchell; g: Gone with the Wind)

1.	(∃x){Nx • Tx • (y)[(Ny • Ty) ⊃ y=x] • Wmx}
2.	Ng • Wmg • (x)[(Nx • Wmx) ⊃ x=g]	
/(∃x){Nx • Tx • (y)[(Ny • Ty) ⊃ y=x] • x=g}
3.	Nc • Tc • (y)[(Ny • Ty) ⊃ y=c] • Wmc		1, EI
4.	(x)[(Nx • Wmx) ⊃ x=g] • Ng • Wmg		2, Com
5.	(x)[(Nx • Wmx) ⊃ x=g]				4, Simp
6.	(Nc • Wmc) ⊃ c=g				5, UI
7.	Nc • Wmc • Tc • (y)[(Ny • Ty) ⊃ y=c]		3, Com
8.	Nc • Wmc					7, Simp
9.	c=g					6+8, MP
10.	Nc • Tc • (y)[(Ny • Ty) ⊃ y=c]			3, Simp
11.	Nc • Tc • (y)[(Ny • Ty) ⊃ y=c] • c=g		10+9, Conj
12.	(∃x){Nx • Tx • (y)[(Ny • Ty) ⊃ y=x] x=g}	11, EG

October 26 Problems

1. Ps • Is • (x)[(Px • Ix) ⊃ x=s]
2. Pc • Lc
3. (∃x)(Px • Ix • ~Lx)		/c≠s

Ronald Reagan was the oldest U.S. president. Woodrow Wilson was
a U.S. president. Woodrow Wilson is not Ronald Reagan. Therefore,
Ronald Reagan was older than Woodrow Wilson. (Ux: x is a U.S. president;
Oxy: x is older than y; r: Ronald Reagan; w: Woodrow Wilson)

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