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
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.
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
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?
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.ACP (Assuming for conditional proof)
didn't use this, but maybe you can to use your rules with itor AIP (Assuming for Indirect Proof)
i have no idea what any of these mean&E , →E , ¬& , ¬v , ¬→ , →v , &C , &A , vC , vA , vE* , →E* ,
[/quote]¬(Biconditional) , →(Biconditional)[/quote]how is it that both these symbols mean the same thing?
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 youthose are the only rules we can use. So is there any way you can solve the problem using on those rules?