SOLUTION: solve plz? with rules of inference and replacement...
1. (~D + A) v (~D + R)
2. D v ~A /∴ K > R
___________ ___________ _______
1. ~(G + M)
2. M v ~G /∴ ~G
________
Algebra ->
Proofs
-> SOLUTION: solve plz? with rules of inference and replacement...
1. (~D + A) v (~D + R)
2. D v ~A /∴ K > R
___________ ___________ _______
1. ~(G + M)
2. M v ~G /∴ ~G
________
Log On
Question 1204272: solve plz? with rules of inference and replacement...
1. (~D + A) v (~D + R)
2. D v ~A /∴ K > R
_______________________________
1. ~(G + M)
2. M v ~G /∴ ~G
_______________________________
I know y'all only answer two questions...but it's worth a shot to ask...If not, thank you anyways!!
1. P = (R + S)
2. P /∴ R = S
You can put this solution on YOUR website!
Normally I would mention that the rule of this website is "one question per post", but the problems aren't too lengthy here.
Problem 1
Number
Statement
Line(s) Used
Reason
1
(~D + A) v (~D + R)
2
D v ~A
:.
K > R
3
~D + (A v R)
1
Distribution
4
~D
3
Simplification
5
~A
2,4
Disjunctive Syllogism
6
A v R
3
Simplification
7
R
6,5
Disjunctive Syllogism
8
R v ~K
7
Addition
9
~K v R
8
Commutation
10
K > R
9
Material Implication
Refer to these rules of inference and replacement https://logiccurriculum.com/2019/02/09/rules-for-proofs/
The notation is slightly different. That reference sheet has a center dot instead of a plus sign. Also, that sheet uses a horsehoe instead of a greater than sign.
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Problem 2
Number
Statement
Line(s) Used
Reason
1
~(G + M)
2
M v ~G
:.
~G
3
~G v ~M
1
De Morgan's Law
4
~G v M
2
Commutation
5
G > ~M
3
Material Implication
6
G > M
4
Material Implication
7
~M > ~G
6
Transposition
8
G > ~G
5,7
Hypothetical Syllogism
9
~G v ~G
8
Material Implication
10
~G
9
Tautology
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Problem 3
Focus on row 2. I've highlighted this in red
The premises P = (R+S) and P are true, but the conclusion is false.
Any time there is a situation with all true premises but a false conclusion, it means the argument is invalid.
Therefore, you would not be able to find a logical derivation when presented with these premises and conclusion. Attempting to do so will have you endlessly searching for something that doesn't exist. It's possible that your teacher made a typo somewhere.
(