# Symbolic Logic Problem (Urgent)

• December 13th 2008, 09:58 PM
dsljrich
Symbolic Logic Problem (Urgent)
I need urgent help with this problem!
I have shown how far I got with it, but now I'm stuck, I dont know what to do next. Someone Please help me out.

∃xMxa & ∀x(Mxa →Kxa); ∀y(Kya → (y =b v y = c)) ∴ ¬Kba →Kca

1. ∃xMxa & ∀x(Mxa →Kxa) A
2. ∀y(Kya → (y =b v y = c)) A
3. Show ¬Kba →Kca
4. ¬Kba ACP
5. Mda & ∀x(Mxa →Kxa) ∃E, 1
6. Mda &E, 5
7. ∀x(Mxa →Kxa) &E, 5
8. Mda →Kda ∀E, 7
9. Kda →E, 6, 8
10. Kda → (d =b v d = c) ∀E, 2
11. (d =b v d = c) →E, 9, 10
12.
• December 13th 2008, 10:35 PM
Jhevon
Quote:

Originally Posted by dsljrich
I need urgent help with this problem!
I have shown how far I got with it, but now I'm stuck, I dont know what to do next. Someone Please help me out.

∃xMxa & ∀x(Mxa →Kxa); ∀y(Kya → (y =b v y = c)) ∴ ¬Kba →Kca

1. ∃xMxa & ∀x(Mxa →Kxa) A
2. ∀y(Kya → (y =b v y = c)) A
3. Show ¬Kba →Kca
4. ¬Kba ACP
5. Mda & ∀x(Mxa →Kxa) ∃E, 1
6. Mda &E, 5
7. ∀x(Mxa →Kxa) &E, 5
8. Mda →Kda ∀E, 7
9. Kda →E, 6, 8
10. Kda → (d =b v d = c) ∀E, 2
11. (d =b v d = c) →E, 9, 10
12.

1. $(\exists x)Mxa \wedge (x)(Mxa \Rightarrow Kxa)$

2. $(y)[Kya \Rightarrow (y = b \vee y = c)] ~~/ \therefore ~~\sim Kba \Rightarrow Kca$

3. $\sim Kba$ assumption

4. $(\exists x)Mxa$ 1, simp.

5. $Mxa$ E.I. assumption

6. $(x)(Mxa \Rightarrow Kxa)$ 1, comm., simp.

7. $Mxa \Rightarrow Kxa$ 6, U.I.

8. $Kxa$ 7,5, M.P.

9. $Kxa \Rightarrow (x = b \vee x = c)$ 2, U.I.

10. $x = b \vee x = c$ 9, 8, M.P.

11. $\sim (x = b)$ 8, 3 I.d.

12. $x = c$ 10, 11 D.S.

13. $Kca$ 8, 12 I.d.

14. $Kca$ 4, 5-13 E.I.

15. $\sim Kba \Rightarrow Kca$ 3-14, C.P.
• December 13th 2008, 10:42 PM
dsljrich
Thank you for your reply and solving the problem BUT I'm only in symbolic logic 1. so we dont use the format you used. we use the one i have written in the my first post. can you please write it in that format Please? that would be a really huge help.
• December 13th 2008, 10:46 PM
Jhevon
Quote:

Originally Posted by dsljrich
Thank you for your reply and solving the problem BUT I'm only in symbolic logic 1. so we dont use the format you used. we use the one i have written in the my first post. can you please write it in that format Please? that would be a really huge help.

what in my format do you not understand?
• December 13th 2008, 10:52 PM
dsljrich
The rules that you are used don't look familiar. Also, in line 5 you jus dropped out Ex without assigning any variable for the x in Mxa. So far we are taught to replace a constant with a variable in ExMxa so it would read Mda. And I dont understand U.I. M.P. I.d. D.S. .. EI .. that im familiar with.
• December 13th 2008, 10:59 PM
Jhevon
Quote:

Originally Posted by dsljrich
The rules that you are used don't look familiar. Also, in line 5 you jus dropped out Ex without assigning any variable for the x in Mxa. So far we are taught to replace a constant with a variable in ExMxa so it would read Mda. And I dont understand U.I. M.P. I.d. D.S. .. EI .. that im familiar with.

when dropping the Ex, you cannot just replace the variable. it doesn't work that way. in line 5 i applied the rule of E.I.

U.I. means universal instatiation
M.P. means Modus Ponens
I.d. means Principle of ideneity, it is the set of rules that go with "="
E.I. means existential instantiation, it is the rule that goes with dropping Ex
D.S. means disjunctive syllogism
comm. means commutativity
simp. means simplification

now hopefully you can translate to the format you want
• December 13th 2008, 11:11 PM
dsljrich
a little confused =/
I haven't learned a lot of those rules yet, that might be why it wasn't clear to me. Is it possible to solve it using existential intro, existential explo. universal explo. quantifier negation, =I, =E and some other basics?
• December 13th 2008, 11:12 PM
dsljrich
We have not learned those rules yet. The rules we use are

∃E , ∀E, ACP (Assuming for conditional proof)
or AIP (Assuming for Indirect Proof) ,
&E , →E , ¬& , ¬v , ¬→ , →v , &C , &A , vC , vA , vE* , →E* , ¬(Biconditional) , →(Biconditional)

those are the only rules we can use. So is there any way you can solve the problem using on those rules?
• December 13th 2008, 11:27 PM
Jhevon
Quote:

Originally Posted by dsljrich
We have not learned those rules yet. The rules we use are

∃E , ∀E,

don't know what these mean. i used (x) to mean $\forall x$.
Quote:

ACP (Assuming for conditional proof)
my first assumption was for conditional proof. that is what C.P. at the end meant. it said lines 3 to 14 were a conditional proof starting with the assumption at line 3.

Quote:

or AIP (Assuming for Indirect Proof)
didn't use this, but maybe you can to use your rules with it

Quote:

&E , →E , ¬& , ¬v , ¬→ , →v , &C , &A , vC , vA , vE* , →E* ,
i have no idea what any of these mean

[/quote]¬(Biconditional) , →(Biconditional)[/quote]how is it that both these symbols mean the same thing?

Quote:

those are the only rules we can use. So is there any way you can solve the problem using on those rules?
the rules i used were not advanced. they are basic rules, in the Rosser's System of logic, as taught in "Symbolic Logic" by Copi. chances are you know these rules, but under different names, and maybe applied slightly differently. for instance, what you call existential and universal intro, i call existential and universal instantiation. when you say "expo" in the same context, i would say "generalization". i am familiar with quantifier negation, but i did not use that here. so unless you describe what your rules mean, i can't help you