2. Using a truth table, show whether the following wffs are satisfiable. B. justification for your conclusion and list the truth sets, if applicable. a. (p→q) ^ (q→p) b. ((p Aq) Ar) ^ ¬r c. ((p^q) vr) V¬r

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Chapter1: Introduction
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Can anyone please help me with question 2 ? I am stuck on it
b. (b→¬a)-((¬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.
5.
a. (((p^q) ^r), (pv q),-p}
b. ((p-q),¬p,¬q}
c. {p.(q-p),(-qV p)}
4. Prove the following by mathematical induction.
TL
Σ
( = 1
n(n + 1)(2n + 1)
6
Prove the following by mathematical induction: n! > 2" for all integers n 24.
Transcribed Image Text:b. (b→¬a)-((¬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. 5. a. (((p^q) ^r), (pv q),-p} b. ((p-q),¬p,¬q} c. {p.(q-p),(-qV p)} 4. Prove the following by mathematical induction. TL Σ ( = 1 n(n + 1)(2n + 1) 6 Prove the following by mathematical induction: n! > 2" for all integers n 24.
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)
((р^q)^r)^ ¬r
b.
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),(-qV p)}
4. Prove the following by mathematical induction.
n n(n+1)(2n + 1)
₁².
6
i=1
5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
Transcribed Image Text: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) ((р^q)^r)^ ¬r b. 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),(-qV p)} 4. Prove the following by mathematical induction. n n(n+1)(2n + 1) ₁². 6 i=1 5. Prove the following by mathematical induction: n! > 2" for all integers n ≥ 4.
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