General Directions. There are four (4) sections to this exam. Please read and fo
ID: 3856435 • Letter: G
Question
General Directions. There are four (4) sections to this exam. Please read and follow all directions carefully. Please do not send your answers in an attachment. Note that ‘->’ is used for conditionals, ‘~’ is used for negations, ‘v’ is used for disjunctions, ‘&’ is used for conjunctions, ‘<->’ is used for biconditionals, and ‘/’ is used as the conclusion indicator.
C. Directions. Use Conditional Proof to prove the following two (2) arguments to be valid.
C.1.
1. (P v P) -> [(E -> R) & (L -> R)]
2. W -> (E v L) / W -> (P -> R)
C.2.
1. [U -> (Q & L)]
2. [D -> (K & S) / [(L -> D) -> (U -> S)]
Explanation / Answer
P v P) -> [(E -> R) & (L -> R)]
[(p v p) ^ [(E -> R) & (L -> R)
Typo:should be r not q Typo:should be solved in the below procedure
[(p v q ) ^ ('p v q) ^ ('q v r)] v r
['(p v q) v '('p v q) v '('q v r)] v r
[('p ^ qq) v (p ^ qq) v (q ^ rr)] v r
[(q ^ 'p) v (q ^ (p v r)] v r///////////communicative
[(q ^ ('p v (p v r))] v r/////////////distributive
[(q ^ (('p v p) v r)] v r//////////////distributive
[q ^ (T v r) ] v r //////////////////complement
[q ^ T] v r ///////////////////////identity
q v r
W -> (E v L) / W -> (P -> R)
W -> (E v L) / W -> (P -> R)
Typo:should be r not q Typo:should be solved in the below procedure
[(p v q ) ^ ('p v q) ^ ('q v r)] v r
['(p v q) v '('p v q) v '('q v r)] v r
[('p ^ qq) v (p ^ qq) v (q ^ rr)] v r
[(q ^ 'p) v (q ^ (p v r)] v r///////////communicative
[(q ^ ('p v (p v r))] v r/////////////distributive
[(q ^ (('p v p) v r)] v r//////////////distributive
[q ^ (T v r) ] v r //////////////////complement
[q ^ T] v r ///////////////////////identity
q v r
[U -> (Q & L)]
W -> (E v L) / W -> (P -> R)
Typo:should be r not q Typo:should be solved in the below procedure
[(p v q ) ^ ('p v q) ^ ('q v r)] v r
['(p v q) v '('p v q) v '('q v r)] v r
[('p ^ qq) v (p ^ qq) v (q ^ rr)] v r
[(q ^ 'p) v (q ^ (p v r)] v r///////////communicative
[(q ^ ('p v (p v r))] v r/////////////distributive
[(q ^ (('p v p) v r)] v r//////////////distributive
[q ^ (T v r) ] v r //////////////////complement
[q ^ T] v r ///////////////////////identity
q v r
[D -> (K & S) / [(L -> D) -> (U -> S)]
W -> (E v L) / W -> (P -> R)
Typo:should be r not q Typo:should be solved in the below procedure
[(p v q ) ^ ('p v q) ^ ('q v r)] v r
['(p v q) v '('p v q) v '('q v r)] v r
[('p ^ qq) v (p ^ qq) v (q ^ rr)] v r
[(q ^ 'p) v (q ^ (p v r)] v r///////////communicative
[(q ^ ('p v (p v r))] v r/////////////distributive
[(q ^ (('p v p) v r)] v r//////////////distributive
[q ^ (T v r) ] v r //////////////////complement
[q ^ T] v r ///////////////////////identity
q v r
Hope it will help you
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