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Steps below show that the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" imply conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let R(x) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) A R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) A R(Linda) Premise (4) C(Linda) (5) R(Linda) from (3) and (4) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) A S(x)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket".

Steps below show that the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" imply conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let R(x) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) A R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) A R(Linda) Premise (4) C(Linda) (5) R(Linda) from (3) and (4) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) A S(x)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket".

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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Steps below show that the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" imply conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let R(x) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) A R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) A R(Linda) Premise (4) C(Linda) (5) R(Linda) from (3) and (4) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) A S(x)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket".
Transcribed Image Text:Steps below show that the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" imply conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let R(x) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) A R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) A R(Linda) Premise (4) C(Linda) (5) R(Linda) from (3) and (4) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) A S(x)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket".
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