e) Explain, in intuitive terms, why "(3! x ES) (p(x))" means the same thing as "(3x ES) [p(x) and ([V u ES] [p(u) ⇒ u = x])]".
e) Explain, in intuitive terms, why "(3! x ES) (p(x))" means the same thing as "(3x ES) [p(x) and ([V u ES] [p(u) ⇒ u = x])]".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
question e)
![DEFINITION 3.14: For any sets A and B, a function from A to B is a set
SCA X B which satisfies the following conditions:
a) (Vue A) (3 ve B) ((u, v) ES), and
b) (VuEA) (V v, we B) ([(u, v) ES and (u, w) ES] ⇒ v = w).
The set A is called the domain of the function, and the set B is called the co-
domain of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc06c0cac-2e9c-4d45-9a45-e5decd8c209b%2Fcea63b0e-0674-43ee-95e2-772b5095e5be%2Fbia9q7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:DEFINITION 3.14: For any sets A and B, a function from A to B is a set
SCA X B which satisfies the following conditions:
a) (Vue A) (3 ve B) ((u, v) ES), and
b) (VuEA) (V v, we B) ([(u, v) ES and (u, w) ES] ⇒ v = w).
The set A is called the domain of the function, and the set B is called the co-
domain of the function.
![b) Rewrite Definition 3.14 using the unique existential quantifier.
c) Suppose f: A → B. Rephrase the quantifier statement
"(VvE B) (3! u EA) (f(u) = v)"
using terminology for functions introduced in this section.
d) Express "~(3! x
S) (p(x))" without using negation except directly next to the
predicate p(x) (careful! this is not easy).
e) Explain, in intuitive terms, why "(3! x ES) (p(x))" means the same thing as
"(3 x S) [p(x) and ([V u ES] [p(u) ⇒ u = x])]".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc06c0cac-2e9c-4d45-9a45-e5decd8c209b%2Fcea63b0e-0674-43ee-95e2-772b5095e5be%2Furexoxe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) Rewrite Definition 3.14 using the unique existential quantifier.
c) Suppose f: A → B. Rephrase the quantifier statement
"(VvE B) (3! u EA) (f(u) = v)"
using terminology for functions introduced in this section.
d) Express "~(3! x
S) (p(x))" without using negation except directly next to the
predicate p(x) (careful! this is not easy).
e) Explain, in intuitive terms, why "(3! x ES) (p(x))" means the same thing as
"(3 x S) [p(x) and ([V u ES] [p(u) ⇒ u = x])]".
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