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a. From the three premises: (P v ~R), (~R-S), and ~P; Prove: S; hint use the definition of disjunction: (p v q) means that p is true, or q is true, or both p and q are true; so that from (p v q) and ~p it follows that q must be true: 1. (P v R) premise 2. (~R→S) premise 3. ~P premise 4. 5. 8

a. From the three premises: (P v ~R), (~R-S), and ~P; Prove: S; hint use the definition of disjunction: (p v q) means that p is true, or q is true, or both p and q are true; so that from (p v q) and ~p it follows that q must be true: 1. (P v R) premise 2. (~R→S) premise 3. ~P premise 4. 5. 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. From the three premises: (P v ~R), (~R-S), and ~P; Prove: S; hint use the definition of disjunction: (p v q) means that p is true, or q is true, or both p and q are true; so that from (p v q) and ~p it follows that q must be true: 1. (P v ~R) premise 2. (~RS) premise 3. ~P premise 4. 5. b. From the three premises: (P→~Q), and ((~Q v R) →~S), (P & T); Prove: S; hint: use the definition of implication: (P→Q) means either P is false or Q is true, (that is, ~P v Q); and use the definition of disjunction. 1. (P- Q) premise 2. ((~Q v R)→ ~S) premise 3. (P& T) premise 4. 5. 6. 7. +
Transcribed Image Text:a. From the three premises: (P v ~R), (~R-S), and ~P; Prove: S; hint use the definition of disjunction: (p v q) means that p is true, or q is true, or both p and q are true; so that from (p v q) and ~p it follows that q must be true: 1. (P v ~R) premise 2. (~RS) premise 3. ~P premise 4. 5. b. From the three premises: (P→~Q), and ((~Q v R) →~S), (P & T); Prove: S; hint: use the definition of implication: (P→Q) means either P is false or Q is true, (that is, ~P v Q); and use the definition of disjunction. 1. (P- Q) premise 2. ((~Q v R)→ ~S) premise 3. (P& T) premise 4. 5. 6. 7. +
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