7.2.xa. Exercise answers
| 1. | a. |
∀x (Fx → Gx)
Everything, x, is such that if Fx [or: F fits x] then Gx
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| b. |
(∀x: Fx) ¬ Gx
Everything, x, such that F x is such that not Gx
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| c. |
∀x ((Fx ∧ ¬ Gx) → Hx)
Everything, x, is such that if both Fx and not Gx then Hx
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| d. |
(∀x: Px ∧ ¬ Rxx) Rxa
Everything, x, such that both Px and not Rxx is such that Rxa
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| e. |
∀x ((Rxa ∧ ¬ Rbx) → ¬ (Fx ∨ Gx))
Everything, x, is such that if both Rxa and not Rbx then not either Fx or Gx
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| f. |
(∀x: Fx ∨ Gx) (Hx ∧ ¬ Kx)
Everything, x, such that either Fx or Gx is such that both Hx and not Kx
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| 2. | a. |
Everyone had heard about the accident
Everyone is such that (he or she had heard about the accident) (∀x: x is a person) x had heard about the accident
(∀x: Px) Hxa
H: [ _ had heard about _ ]; P: [ _ is a person]; a: the accident
∀x (Px → Hxa) |
| b. |
Every relative of Sam agreed with him about the issue Every relative of Sam is such that (he or she agreed with Sam about the issue) (∀x: x is a relative of Sam) x agreed with Sam about the issue
(∀x: Rxs) Axsi
A: [ _ agreed with _ about _ ]; R: [ _ is a relative of _ ]; i: the issue; s: Sam |
| c. |
Edna took pleasure in none of her possessions No possession of Edna is such that (Edna took pleasure in it) (∀x: x is a possession of Edna) ¬ Edna took pleasure in x
(∀x: Pxe) ¬ Lex
L: [ _ took pleasure in _ ]; P: [ _ is a possession of _ ]; e: Edna |
| d. |
Tom found only empty boxes Among boxes, only empty ones are such that (Tom found them) (∀x: x is a box ∧ ¬ x is empty) ¬ Tom found x
(∀x: Bx ∧ ¬ Ex) ¬ Ftx
B: [ _ is a box]; E: [ _ is empty]; F: [ _ found _ ]; t: Tom |
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| e. |
The survey was sent to all members of the organization except its officers All members of the organization except the organization’s officers are such that (the survey was sent to them) (∀x: x is a member of the organization ∧ ¬ x is an officer of the organization) the survey was sent to x
(∀x: Mxo ∧ ¬ Oxo) Ssx
M: [ _ is a member of _ ]; O: [ _ is an officer of _ ]; S: [ _ was sent to _ ]; o: the organization; s: the survey |
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| f. |
Only countries bordering the Pacific will prosper Among countries, only those bordering the Pacific are such that (they will prosper) (∀x: x is a country ∧ ¬ x borders the Pacific) ¬ x will prosper
(∀x: Cx ∧ ¬ Bxp) ¬ Px
B: [ _ borders _ ]; C: [ _ is a country]; P: [ _ will prosper]; p: the Pacific |
| 3. | a. |
(∀x: x is a dog) x chases cats Every dog is such that (it chases cats) Every dog chases cats (or: All dogs chase cats; or: Dogs chase cats) |
| b. |
(∀x: x is a hole) Holly patched x Every hole is such that (Holly patched it) Holly patched every hole (or: Holly patched each hole) |
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| c. |
(∀x: x is a person) ¬ x volunteered No one is such that (he or she volunteered) No one volunteered. |
| d. |
(∀x: ¬ x is a cockroach) ¬ x will survive Only cockroaches are such that (they will survive) Only cockroaches will survive |
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| e. |
∀x ¬ x seemed right Nothing is such that (it seemed right) Nothing seemed right |
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| f. |
(∀x: x was a reviewer ∧ ¬ x was a friend of the director) x panned the movie All reviewers except friends of the director are such that (they panned the movie) All reviewers except friends of the director panned the movie (or: Among reviewers, all but friends of the director panned the movie) |
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| g. |
(∀x: x is a bird ∧ ¬ x is an early bird) ¬ x gets a worm Among birds, only early ones are such that (they get worms) Only early birds get worms (or: No birds except early ones get worms) |
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| h. |
(∀x: ¬ x is a small child) the movie bored x All things except small children are such that (the movie bored them) The movie bored all but small children |