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
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
asked Aug 26 at 19:57
user3352632
827
add a comment |Â
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
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
asked Aug 26 at 19:57
user3352632
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
add a comment |Â
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
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
asked Aug 26 at 19:57
user3352632
827
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
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
asked Aug 26 at 19:57
user3352632
827
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
edited Aug 26 at 20:30
Jendrik Stelzner
7,63121037
7,63121037
asked Aug 26 at 19:57
user3352632
827
asked Aug 26 at 19:57
user3352632
827
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
add a comment |Â
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
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
The calculus is correct. Â 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. Â 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: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$
answered Aug 26 at 21:36
Graham Kemp
81k43275
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
The calculus is correct. Â 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. Â 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: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$
answered Aug 26 at 21:36
Graham Kemp
81k43275
add a comment |Â
up vote
1
down vote
The calculus is correct. Â 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. Â 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: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$
answered Aug 26 at 21:36
Graham Kemp
81k43275
add a comment |Â
up vote
1
down vote
up vote
1
down vote
The calculus is correct. Â 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. Â 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: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$
answered Aug 26 at 21:36
Graham Kemp
81k43275
The calculus is correct. Â 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. Â 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: $Awedge(Avee C)to(Cvee B)\equiv Ato (Cvee B)\equiv neg Avee Cvee B$
answered Aug 26 at 21:36
Graham Kemp
81k43275
answered Aug 26 at 21:36
Graham Kemp
81k43275
answered Aug 26 at 21:36
Graham Kemp
81k43275
answered Aug 26 at 21:36
Graham Kemp
81k43275
81k43275
add a comment |Â
add a comment |Â
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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