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3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} {(p-q), p, q} b. c. {p.(q-p),(-q V p)}

3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} {(p-q), p, q} b. c. {p.(q-p),(-q V p)}

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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Can anyone please help me with questions 3? I’m stuck on it
prys 150 3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} b. {(p-q),¬p,¬q} c. {p,(q-p),(-q V p)} 4. Prove the following by mathematical induction. n Σ i = 1 n(n + 1)(2n + 1) 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
Transcribed Image Text:prys 150 3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} b. {(p-q),¬p,¬q} c. {p,(q-p),(-q V p)} 4. Prove the following by mathematical induction. n Σ i = 1 n(n + 1)(2n + 1) 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
c. ((p^q) vr) v¬r 3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} b. {(p-q),¬p,¬q} c. {p,(q-p),(-q V p)} 4. Prove the following by mathematical induction. n i=1 .2 n(n + 1)(2n + 1) 6 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
Transcribed Image Text:c. ((p^q) vr) v¬r 3. Using a truth table, show which of the following sets of formula are satisfiable. Be sure to state your justification for your conclusion. a. {((p^q) ^r), (pv q),¬p} b. {(p-q),¬p,¬q} c. {p,(q-p),(-q V p)} 4. Prove the following by mathematical induction. n i=1 .2 n(n + 1)(2n + 1) 6 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
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