Where is the mistake in the following proof?
1)(?x)(Fx · Ax)
2.(?x)(Fx · Ox)
3.? (?x)(Ax · Ox)
4.Fb · Ab (1, E.I.)
5.Fb · Ob (2, E.I.)
6.Ab · Fb (4, Com.)
7.Ab (6, Simp.)
8.Ob · Fb (5, Com.)
9.Ob (8, Simp.)
10.Ab · Ob (7, 9, Conj.)
11.(?x)(Ax · Ox) (10, E.G.)

A)line 4
B)line 8
C)line 5
D)line 9

Question

Where is the mistake in the following proof?
1)(?x)(Fx · Ax) 
2.(?x)(Fx · Ox) 
3.? (?x)(Ax · Ox) 
4.Fb · Ab (1, E.I.) 
5.Fb · Ob (2, E.I.) 
6.Ab · Fb (4, Com.) 
7.Ab (6, Simp.) 
8.Ob · Fb (5, Com.) 
9.Ob (8, Simp.) 
10.Ab · Ob (7, 9, Conj.) 
11.(?x)(Ax · Ox) (10, E.G.)

A)line 4
B)line 8
C)line 5
D)line 9

Quizplus · Accepted Answer

The mistake is in line 5. The existential instantiation (E.I.) used in line 5 incorrectly assumes that the same individual 'b' that satisfies Fx · Ax also satisfies Fx · Ox, which is not logically guaranteed by the premises.

Where Is the Mistake in the Following Proof