
Applied Math Applied Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 2nd, 2016, 03:56 AM  #1 
Member Joined: Jan 2016 From: / Posts: 35 Thanks: 1  Am I doing this right? (Predicate logic)
Hey thanks for checking the thread! So i have to prove a conclusion is true with predicate logic I don't have a step by step solution so i tried myself That's my problem : Conclusion : ∃x : ¬Q(x) Premises : 1.∀ : x (P(x) → ∀y : (Q(x) → R(x,y))) 2 ∃x : (P(x) ∧ ∃y : ¬R(x,y)) 3. ∃x ∃y [ P(x) ∧ ¬R(x,y)] (pulled out quantifiers) 4. ∃x [ P(x) ∧ ¬R(x,b)] EI(3), not sure if it's right 5. P(a) ∧ ¬R(a,b) EI(4) 6. P(a) Simp(5) 7. ¬R(a,b) Simp(5) 8. ∀x ∀y [ P(x) → Q(x) → R(x,y) ] pulled out quantifiers 9. ∀x [ P(x) → Q(x) → R(x,b) ] UI [8] 10. P(a) → Q(a) → R(a,b) UI[9] 11. All three parts have implication between them therefore i can switch order of operations like this : ( P(a) → Q(a) ) → R(a,b) 12. ( ¬ P(a) ∨ Q(a) ) → R(a,b) solved the inner parentheses with Impl1 rule 13. ¬ ( ¬ P(a) ∨ Q(a)) ∨ R(a,b) same rule for outer one 14. ( P(a) ∧ ¬Q(a) ) ∨ R(a,b) De Morgan's + double negation, keeping the second part the same. 15. ( R(a,b) v ¬Q(a) ) ∧ ( R(a,b) v P(a)) distributive law 16. R(a,b) v ¬Q(a) Simp(15) 17. R(ab) v P(a) Simp(15) 18. ¬Q(a) disjunctive syllogism (16,7) 19 ∃x : ¬Q(x) EG[1,8] First, If you had time to follow all this thank you in advance! Now i'd like to know whether this is solved correctly? Did I make aNY mistakeS and if I did, please show me where and point me in the right direction! Last edited by SuperNova1250; August 2nd, 2016 at 03:59 AM. 
August 3rd, 2016, 11:51 PM  #2 
Member Joined: Jan 2016 From: / Posts: 35 Thanks: 1 
Can anyone please help me with this problem, i'm stuck! Thanks! 

Tags 
logic, predicate 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Predicate Logic Problem  programmer123  Applied Math  5  August 24th, 2015 06:48 PM 
predicate logic  skaur  Applied Math  1  January 6th, 2014 05:51 PM 
Predicate Logic  mohitpd  Applied Math  0  October 26th, 2013 07:45 PM 
Predicate Logic  pavankumar.thati  Applied Math  0  April 16th, 2013 09:26 AM 
Resolution in Predicate logic  Leila  Applied Math  9  January 4th, 2011 05:54 AM 