Results 1 to 9 of 9

Math Help - Symbolic Logic Problem (Urgent)

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    5

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dsljrich View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    5
    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.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dsljrich View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2008
    Posts
    5
    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.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dsljrich View Post
    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
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Dec 2008
    Posts
    5

    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?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Dec 2008
    Posts
    5
    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?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dsljrich View Post
    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.
    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.

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

    &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?

    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conceptual Questions for Modern Symbolic Logic
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: December 11th 2011, 10:56 AM
  2. Symbolic Logic Help
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 9th 2010, 01:25 AM
  3. Symbolic Logic Proof Help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 27th 2009, 02:54 AM
  4. Symbolic Logic Proofs
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 07:56 PM
  5. Symbolic Logic help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 11th 2008, 03:56 AM

Search Tags


/mathhelpforum @mathhelpforum