SOLUTION: please solve: 1. (K v S) v (T v W) 2. ~S + [T v ~(O v Z)] 3. K > ~(T v ~Z) /∴ T v W 1. (A > O) v (Z + ~T) 2. ~Z + ~O /∴ ~[(A v Z) + K]

Question 1204165: please solve:
1. (K v S) v (T v W)
2. ~S + [T v ~(O v Z)]
3. K > ~(T v ~Z) /∴ T v W

1. (A > O) v (Z + ~T)
2. ~Z + ~O /∴ ~[(A v Z) + K]
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

1. (K v S) v (T v W)
2. ~S + [T v ~(O v Z)]
3. K > ~(T v ~Z) /∴ T v W

4.            | ~(T v W)            Assumption for Indirect Proof
5.            | (T v W) v (K v S)   1, Commutation 
6.            | K v S               5,4 Disjunctive Syllogism
7.            | S v K               6, Commutation
8.            | ~S                  2, Simplification
9.            | K                   7,8, Disjunctive Syllogism
10.           | ~(T v ~Z)           3,9, Modus Ponens 
11.           | ~T + ~~Z            10, DeMorgan's Law
12.           | ~T + Z              11, Double Negation
13.           | Z + ~T              12, Commutation 
14.           | Z                   13, Simplification
15.           | [T v ~(O v Z)] + ~S  2, Commutation
16.           | T v ~(O v Z)        15, Simplification
17.           | ~T                  12, Simplification
18.           | ~(O v Z)            16,17, Disjunctive Syllogism
19.           | ~O + ~Z             17, DeMorgan's Law
20.           | ~Z + ~O             18, Commutation
21.           | ~Z                  19, Simplification
22.           | Z + ~Z              13,19, Conjunction
23. T v W    Lines 4-23 Indirect Proof       

Edwin

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