Are my DNF and CNF for $A land (A lor C) implies (C lor B)$ correct?

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Is this calucation of DNF and CNF for the formula $A land (A lor C) implies (C lor B)$ correct?
$$
beginarray
hline
textGiven:
& A land (A lor C) implies (C lor B)
\
hline

& (neg(A land (A lor C)) lor (C lor B))
\
hline

& (neg A lor neg(A lor C) lor (C lor B))
\
hline

& (neg A lor (neg A land neg C) lor (C vee B))
\
hline
textDNF:
& neg A lor (neg A land neg C) lor C lor B
\
hline

& neg A lor (C lor B)
\
hline
textDNF and CNF:
& neg A lor C lor B
\
hline
endarray
$$
(Original picture of the calculation here.)



When I got the DNF, I applied the absorption rule in order to get DNF/CNF.




logic propositional-calculus conjunctive-normal-form disjunctive-normal-form




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  • Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
    – user3352632
    Aug 26 at 20:41











  • It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
    – Jendrik Stelzner
    Aug 26 at 20:55














up vote
3
down vote

favorite












Is this calucation of DNF and CNF for the formula $A land (A lor C) implies (C lor B)$ correct?
$$
beginarray
hline
textGiven:
& A land (A lor C) implies (C lor B)
\
hline

& (neg(A land (A lor C)) lor (C lor B))
\
hline

& (neg A lor neg(A lor C) lor (C lor B))
\
hline

& (neg A lor (neg A land neg C) lor (C vee B))
\
hline
textDNF:
& neg A lor (neg A land neg C) lor C lor B
\
hline

& neg A lor (C lor B)
\
hline
textDNF and CNF:
& neg A lor C lor B
\
hline
endarray
$$
(Original picture of the calculation here.)



When I got the DNF, I applied the absorption rule in order to get DNF/CNF.




logic propositional-calculus conjunctive-normal-form disjunctive-normal-form




share|cite|improve this question






















  • Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
    – user3352632
    Aug 26 at 20:41











  • It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
    – Jendrik Stelzner
    Aug 26 at 20:55












up vote
3
down vote

favorite









up vote
3
down vote

favorite











Is this calucation of DNF and CNF for the formula $A land (A lor C) implies (C lor B)$ correct?
$$
beginarray
hline
textGiven:
& A land (A lor C) implies (C lor B)
\
hline

& (neg(A land (A lor C)) lor (C lor B))
\
hline

& (neg A lor neg(A lor C) lor (C lor B))
\
hline

& (neg A lor (neg A land neg C) lor (C vee B))
\
hline
textDNF:
& neg A lor (neg A land neg C) lor C lor B
\
hline

& neg A lor (C lor B)
\
hline
textDNF and CNF:
& neg A lor C lor B
\
hline
endarray
$$
(Original picture of the calculation here.)



When I got the DNF, I applied the absorption rule in order to get DNF/CNF.




logic propositional-calculus conjunctive-normal-form disjunctive-normal-form




share|cite|improve this question














Is this calucation of DNF and CNF for the formula $A land (A lor C) implies (C lor B)$ correct?
$$
beginarray
hline
textGiven:
& A land (A lor C) implies (C lor B)
\
hline

& (neg(A land (A lor C)) lor (C lor B))
\
hline

& (neg A lor neg(A lor C) lor (C lor B))
\
hline

& (neg A lor (neg A land neg C) lor (C vee B))
\
hline
textDNF:
& neg A lor (neg A land neg C) lor C lor B
\
hline

& neg A lor (C lor B)
\
hline
textDNF and CNF:
& neg A lor C lor B
\
hline
endarray
$$
(Original picture of the calculation here.)



When I got the DNF, I applied the absorption rule in order to get DNF/CNF.





logic propositional-calculus conjunctive-normal-form disjunctive-normal-form





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 26 at 20:30









Jendrik Stelzner

7,63121037




7,63121037










asked Aug 26 at 19:57









user3352632

827




827











  • Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
    – user3352632
    Aug 26 at 20:41











  • It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
    – Jendrik Stelzner
    Aug 26 at 20:55
















  • Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
    – user3352632
    Aug 26 at 20:41











  • It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
    – Jendrik Stelzner
    Aug 26 at 20:55















Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
– user3352632
Aug 26 at 20:41





Thanks for your correction @Jendrik Stelzner - did you also check the calculations?
– user3352632
Aug 26 at 20:41













It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
– Jendrik Stelzner
Aug 26 at 20:55




It has been some time since I’ve dealt with DNF/CNF, but your calculations seem correct to me. But I would prefer it if someone with more expertise would post an answer.
– Jendrik Stelzner
Aug 26 at 20:55










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The calculus is correct.   You can also check the final answer to be sure it is an equivalence.



If $A$ is false, $Awedge(Avee C)to(Cvee B)$ is true, as is the case when either $C$ or $B$ is true.   So if and only if $neg Avee Bvee C$ do we have the implication.



Note also an easier route would have been to apply absorption equivalence first, then implication equivalence: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$






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    The calculus is correct.   You can also check the final answer to be sure it is an equivalence.



    If $A$ is false, $Awedge(Avee C)to(Cvee B)$ is true, as is the case when either $C$ or $B$ is true.   So if and only if $neg Avee Bvee C$ do we have the implication.



    Note also an easier route would have been to apply absorption equivalence first, then implication equivalence: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$






    share|cite|improve this answer
























      up vote
      1
      down vote













      The calculus is correct.   You can also check the final answer to be sure it is an equivalence.



      If $A$ is false, $Awedge(Avee C)to(Cvee B)$ is true, as is the case when either $C$ or $B$ is true.   So if and only if $neg Avee Bvee C$ do we have the implication.



      Note also an easier route would have been to apply absorption equivalence first, then implication equivalence: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        The calculus is correct.   You can also check the final answer to be sure it is an equivalence.



        If $A$ is false, $Awedge(Avee C)to(Cvee B)$ is true, as is the case when either $C$ or $B$ is true.   So if and only if $neg Avee Bvee C$ do we have the implication.



        Note also an easier route would have been to apply absorption equivalence first, then implication equivalence: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$






        share|cite|improve this answer












        The calculus is correct.   You can also check the final answer to be sure it is an equivalence.



        If $A$ is false, $Awedge(Avee C)to(Cvee B)$ is true, as is the case when either $C$ or $B$ is true.   So if and only if $neg Avee Bvee C$ do we have the implication.



        Note also an easier route would have been to apply absorption equivalence first, then implication equivalence: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 26 at 21:36









        Graham Kemp

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