question e) DEFINITION 3.14: For any sets A and B, a function from A to B is a setSCA X B which satisfies the following conditions:a) (Vue A) (3 ve B) ((u, v) ES), andb) (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! xS) (p(x))" without using negation except directly next to thepredicate 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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Answered: e) Explain, in intuitive terms, why…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 38E

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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])]".