Question

Consider the following reduction ad absurdum proof in propositional logic. A combination of derivation lines (to the left, after the line numbers) are and justification lines (to the right) are missing. Fill in the blanks. 1. (A v B) ? (C . D) Premise 2. C ? ~ D Premise/ Show ~ A 3. A Assumption for purposes of indirect proof 4. ___ 3, Add 5. C . D 1, 4, MP 6. C 5, Simp 7. ~ D ___ 8. D 8, Simp 9. D . ~ D 7, 8, Conj 10. A ? (D . ~ D) 3– 9, Indirect Proof A v B; 2,6, MP; NC; ~ A A . B; 2,5 MP; DM, 9,10 MP A ? B; 2,6 MP; 2 DN; ~ A A . B; 2,5 MP; NC; 9,10 DN 

          Consider the following reduction ad
absurdum proof in propositional logic. A
combination of derivation lines (to the left,
after the line numbers) are and justification
lines (to the right) are missing. Fill in the
blanks.

1. (A v B) ? (C . D) Premise
2. C ? ~ D Premise/ Show ~ A
3. A Assumption for
purposes of indirect proof
4. ___ 3, Add
5. C . D 1, 4, MP
6. C 5, Simp
7. ~ D ___
8. D 8, Simp
9. D . ~ D 7, 8, Conj
10. A ? (D . ~ D) 3– 9, Indirect Proof

A v B; 2,6, MP; NC; ~ A
A . B; 2,5 MP; DM, 9,10 MP
A ? B; 2,6 MP; 2 DN; ~ A
A . B; 2,5 MP; NC; 9,10 DN
Show more…
Consider the following reduction ad absurdum proof in propositional logic. A combination of derivation lines (to the left, after the line numbers) are and justification lines (to the right) are missing. Fill in the blanks. 1. (A v B) ? (C . D) Premise 2. C ?   D Premise/ Show   A 3. A Assumption for purposes of indirect proof 4. 3, Add 5. C . D 1, 4, MP 6. C 5, Simp 7.   D 8. D 8, Simp 9. D .   D 7, 8, Conj 10. A ? (D .   D) 3– 9, Indirect Proof A v B; 2,6, MP; NC;   A A . B; 2,5 MP; DM, 9,10 MP A ? B; 2,6 MP; 2 DN;   A A . B; 2,5 MP; NC; 9,10 DN

Added by Jennifer C.

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Mathematical Structures for Computer Science: A Modern Treatment of Discrete Mathematics
Mathematical Structures for Computer Science: A Modern Treatment of Discrete Mathematics
Judith L. Gersting 5th Edition
Chapter 1
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Consider the following reduction ad absurdum proof in propositional logic. A combination of derivation lines (to the left, after the line numbers) and justification lines (to the right) are missing. Fill in the blanks. 1. (A v B) ⊃ (C . D) Premise 2. C ⊃ ~ D Premise/ Show ~ A 3. A Assumption for purposes of indirect proof 4. ___ 3, Add 5. C . D 1, 4, MP 6. C 5, Simp 7. ~ D ___ 8. D 8, Simp 9. D . ~ D 7, 8, Conj 10. A ⊃ (D . ~ D) 3– 9, Indirect Proof A v B; 2,6, MP; NC; ~ A A . B; 2,5 MP; DM, 9,10 MP A ⊃ B; 2,6 MP; 2 DN; ~ A A . B; 2,5 MP; NC; 9,10 DN
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Transcript

-
00:01 In this question we have been given a reduction add absalom proof in the propositional logic.
00:06 Okay, so here it is a problem which is based on the proof of a given propositional logic.
00:17 We need to find out the fill in the blanks with the correct option.
00:20 So first of all, we have our argument as a or b...
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