Match the following sentences expressed in first-order logic to their English counterparts: 1.∀ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y)) 2.∀ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y)) 3.∃ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y)) 4.∃ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y)) Options are 1.Someone owns a piano and plays it 2.Everyone who owns a piano plays it 3.Somebody plays all the piano he owns. 4.Everybody owns a piano and plays it. Refer figure
Match the following sentences expressed in first-order logic to their English counterparts: 1.∀ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y)) 2.∀ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y)) 3.∃ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y)) 4.∃ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y)) Options are 1.Someone owns a piano and plays it 2.Everyone who owns a piano plays it 3.Somebody plays all the piano he owns. 4.Everybody owns a piano and plays it. Refer figure
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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Question
Match the following sentences expressed in first-order logic to their English counterparts:
1.∀ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y))
2.∀ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y))
3.∃ x ∀ y (Piano(y) ∧ Owns(x, y) → Plays(x, y))
4.∃ x ∃ y (Piano(y) ∧ Owns(x, y) ∧ Plays(x, y))
Options are
1.Someone owns a piano and plays it
2.Everyone who owns a piano plays it
3.Somebody plays all the piano he owns.
4.Everybody owns a piano and plays it.
Refer figure
Transcribed Image Text:Match the following sentences expressed in first-order logic to their
English counterparts:
KAXA
(Piano (y) A
Owns (x, y) -
Choose.
Plays (x, у))
V x 3 y
(Piano (y) A
Choose.
Owns (x, у) Л
Plays (x, y))
3 x v y
(Piano(y) A
Choose.
Owns (x, y) -
Plays (x, y))
3 x 3 y
(Piano (y) A
Owns (x, y) A
Choose.
Plays (x, y))
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