Assume that A and B are known to be true, X, Y, and Z are known to be false, and that the truth values of P and Q are unknown. For each of the following statements, state whether it is true or false (you have sufficient information even with the unknowns). 1) ~A v X 2) A →X 3) ~(A v Y) • (B v X) 4) (X → Y) →Z 5) [(A • X) v (~A• ~X)] → [(A → X) • (X → A)] 6) ~{[(~A • B) • (~X •Z)] • ~[(A • ~B) v ~(~Y • ~Z)]} 7) P→ A 8) ~ (P• Q) v P 9) (P → X) → (~X → ~P) 10) [P v (Q • X)] • ~[(P v Q) • (P v X)] 11) [P → (A v X)] → [(P → A) → X)] 12) ~[(P • Q) v (Q • ~P)] • ~[(P • ~Q) v (~Q • ~P)] Translate the following statements into symbolic form using the following scheme of abbreviations: M: Gregory is moral; B: Gregory is beautiful; L: Natalie is lucky 1) Either Gregory is moral and beautiful or Natalie is lucky. 2) If Gregory is moral or beautiful, then Natalie is lucky. 3) If and only if Gregory is neither beautiful nor moral is Natalie not lucky. 4) Gregory is not both moral and beautiful. Translate the following statements into symbolic form using the following scheme of abbreviations: P: God is all powerful; A: God is able to prevent evil; G: God is all good; W: God wants to prevent evil; E: Evil exists; I: There is a God 1) If God is all powerful, she is able to prevent evil, and if she is all good, she wants to prevent evil. 2) Evil doesn't exist unless either God is unable, or doesn’t want, to prevent it, or there is no God. 3) If there is a God, she is all good and all powerful. 4) Evil exists only if there is no God.
Assume that A and B are known to be true, X, Y, and Z are known to be false, and that the truth values of P and Q are unknown. For each of the following statements, state whether it is true or false (you have sufficient information even with the unknowns). 1) ~A v X 2) A →X 3) ~(A v Y) • (B v X) 4) (X → Y) →Z 5) [(A • X) v (~A• ~X)] → [(A → X) • (X → A)] 6) ~{[(~A • B) • (~X •Z)] • ~[(A • ~B) v ~(~Y • ~Z)]} 7) P→ A 8) ~ (P• Q) v P 9) (P → X) → (~X → ~P) 10) [P v (Q • X)] • ~[(P v Q) • (P v X)] 11) [P → (A v X)] → [(P → A) → X)] 12) ~[(P • Q) v (Q • ~P)] • ~[(P • ~Q) v (~Q • ~P)] Translate the following statements into symbolic form using the following scheme of abbreviations: M: Gregory is moral; B: Gregory is beautiful; L: Natalie is lucky 1) Either Gregory is moral and beautiful or Natalie is lucky. 2) If Gregory is moral or beautiful, then Natalie is lucky. 3) If and only if Gregory is neither beautiful nor moral is Natalie not lucky. 4) Gregory is not both moral and beautiful. Translate the following statements into symbolic form using the following scheme of abbreviations: P: God is all powerful; A: God is able to prevent evil; G: God is all good; W: God wants to prevent evil; E: Evil exists; I: There is a God 1) If God is all powerful, she is able to prevent evil, and if she is all good, she wants to prevent evil. 2) Evil doesn't exist unless either God is unable, or doesn’t want, to prevent it, or there is no God. 3) If there is a God, she is all good and all powerful. 4) Evil exists only if there is no God.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Question
![Assume that A and B are known to be true, X, Y, and Z are known to be false, and that
the truth values of P and Q are unknown. For each of the following statements, state
whether it is true or false (you have sufficient information even with the unknowns).
1) ~A v X
2) A → X
3) ~(A v Y) • (B v X)
4) (X → Y)→Z
5) [(A • X) v (~A • ~X)] → [(A → X) • (X → A)1
6) ~{[(~A • B) • (~X • Z)] • ~[(A • ~B) v ~(~Y • ~Z)]}
7) P→ A
8) ~ (P • Q) v P
9) (Р —> X) —> (~X > ~Р)
10) [P v (Q • X)] • ~[(P v Q) • (P v X)]
11) [P → (A v X)] → [(P → A) → X)]
12) ~[(P • Q) v (Q • ~P)] • ~[(P • ~Q) v (~Q • ~P)]
Translate the following statements into symbolic form using the following scheme of
abbreviations: M: Gregory is moral; B: Gregory is beautiful; L: Natalie is lucky
1) Either Gregory is moral and beautiful or Natalie is lucky.
2) If Gregory is moral or beautiful, then Natalie is lucky.
3) If and only if Gregory is neither beautiful nor moral is Natalie not lucky.
4) Gregory is not both moral and beautiful.
Translate the following statements into symbolic form using the following scheme of
abbreviations: P: God is all powerful; A: God is able to prevent evil; G: God is all good;
W: God wants to prevent evil; E: Evil exists; I: There is a God
1) If God is all powerful, she is able to prevent evil, and if she is all good, she wants
to prevent evil.
2) Evil doesn't exist unless either God is unable, or doesn't want, to prevent it, or
there is no God.
3) If there is a God, she is all good and all powerful.
4) Evil exists only if there is
God.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46d7a445-a0b6-4898-a4df-bd211d1e95a1%2F80625774-9bb6-48ff-81ac-61957f47f8d1%2Frh2zp_processed.png&w=3840&q=75)
Transcribed Image Text:Assume that A and B are known to be true, X, Y, and Z are known to be false, and that
the truth values of P and Q are unknown. For each of the following statements, state
whether it is true or false (you have sufficient information even with the unknowns).
1) ~A v X
2) A → X
3) ~(A v Y) • (B v X)
4) (X → Y)→Z
5) [(A • X) v (~A • ~X)] → [(A → X) • (X → A)1
6) ~{[(~A • B) • (~X • Z)] • ~[(A • ~B) v ~(~Y • ~Z)]}
7) P→ A
8) ~ (P • Q) v P
9) (Р —> X) —> (~X > ~Р)
10) [P v (Q • X)] • ~[(P v Q) • (P v X)]
11) [P → (A v X)] → [(P → A) → X)]
12) ~[(P • Q) v (Q • ~P)] • ~[(P • ~Q) v (~Q • ~P)]
Translate the following statements into symbolic form using the following scheme of
abbreviations: M: Gregory is moral; B: Gregory is beautiful; L: Natalie is lucky
1) Either Gregory is moral and beautiful or Natalie is lucky.
2) If Gregory is moral or beautiful, then Natalie is lucky.
3) If and only if Gregory is neither beautiful nor moral is Natalie not lucky.
4) Gregory is not both moral and beautiful.
Translate the following statements into symbolic form using the following scheme of
abbreviations: P: God is all powerful; A: God is able to prevent evil; G: God is all good;
W: God wants to prevent evil; E: Evil exists; I: There is a God
1) If God is all powerful, she is able to prevent evil, and if she is all good, she wants
to prevent evil.
2) Evil doesn't exist unless either God is unable, or doesn't want, to prevent it, or
there is no God.
3) If there is a God, she is all good and all powerful.
4) Evil exists only if there is
God.
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