Essentials of DISCRETE MATHEMATICSSection 1.3 - Predicate Logic (a) Write the following statements in predicate logic.1. All sports cars are fast.ii. There are fast cars that aren't sports cars.iii. Every fast sports car is expensive.(b) Write the following predicate logic statement in everyday English.Don't just give a word-for-word translation; your sentence shouldmake sense.)S(x) → (3y)(E(y) ^ A(y, x))]->(c) Formally negate the statement from part (b). Simplify your negationso that no quantifier or connective lies within the scope of a negation.State which derivation rules you are using.(d) Give a translation of your negated statement in everyday English. 2 Let the following predicates be given. The domain is all carsF(x) = "x is fast."66S(x) = "x is a sports car."66E(x) = "x is expensive."66%3DA(x, y) = "x is safer than y.66%3D

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Description: Essentials of DISCRETE MATHEMATICSSection 1.3 - Predicate Logic (a) Write the following statements in predicate logic.1. All sports cars are fast.ii. There are fast cars that aren't sports cars.iii. Every fast sports car is expensive.(b) Write the fo

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Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Essentials of DISCRETE MATHEMATICS

Section 1.3 - Predicate Logic

(a) Write the following statements in predicate logic.
1. All sports cars are fast.
ii. There are fast cars that aren't sports cars.
iii. Every fast sports car is expensive.
(b) Write the following predicate logic statement in everyday English.
Don't just give a word-for-word translation; your sentence should
make sense.
)S(x) → (3y)(E(y) ^ A(y, x))]
->
(c) Formally negate the statement from part (b). Simplify your negation
so that no quantifier or connective lies within the scope of a negation.
State which derivation rules you are using.
(d) Give a translation of your negated statement in everyday English.

2 Let the following predicates be given. The domain is all cars
F(x) = "x is fast."
66
S(x) = "x is a sports car."
66
E(x) = "x is expensive."
66
%3D
A(x, y) = "x is safer than y.
66
%3D

Expert Solution

Step 1

Given that

$F (x) = " x i s f a s t " S (x) = " x i s a s p o r t s c a r " E (x) = " x i s e x p e n s i v e " A (x, y) = " x i s s a f e r t h a n y "$

To find (a), (b):

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