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1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pvq)^(p-r) b. (ba)-((¬b→a)→b)

1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pvq)^(p-r) b. (ba)-((¬b→a)→b)

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 1,2,3,4 and 5 ? I’m stuck on them!
Wednesday, 3/1/2023. The assessment will be closed book and closed note. 1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pvq)^(p-r) b. (ba)-((¬b→a)→b) 2. Using a truth table, show whether the following wffs are satisfiable. Be sure to state your justification for your conclusion and list the truth sets, if applicable. a. (p→q) ^ (q→p) b. ((p^q) ^r) ^¬r 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(n + 1)(2n + 1) Σ2²: 6 1=1 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
Transcribed Image Text:Wednesday, 3/1/2023. The assessment will be closed book and closed note. 1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pvq)^(p-r) b. (ba)-((¬b→a)→b) 2. Using a truth table, show whether the following wffs are satisfiable. Be sure to state your justification for your conclusion and list the truth sets, if applicable. a. (p→q) ^ (q→p) b. ((p^q) ^r) ^¬r 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(n + 1)(2n + 1) Σ2²: 6 1=1 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
book and closed note. 1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pv q) ^ (por) b. (ba)-((-b→a)→b) 2. Using a truth table, show whether the following wffs are satisfiable. Be sure to state your justification for your conclusion and list the truth sets, if applicable. a. (p→q) ^ (q→p) b. ((p^q)^r) A-r 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 n(n+1)(2n + 1) 6 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4. i=1
Transcribed Image Text:book and closed note. 1. Using a truth table, show whether the following wffs are tautologies. Be sure to state your justification for your conclusion. a. (pv q) ^ (por) b. (ba)-((-b→a)→b) 2. Using a truth table, show whether the following wffs are satisfiable. Be sure to state your justification for your conclusion and list the truth sets, if applicable. a. (p→q) ^ (q→p) b. ((p^q)^r) A-r 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 n(n+1)(2n + 1) 6 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4. i=1
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