Question a c) Are there surjeThere is a third quantifier, called the "unique existence" quantifier, which is used to abbrevi-ate statements like the definition of "function" (Definition 3.14). The symbol for this quantifieris "3!", the existential quantifier followed by an exclamation point. It is defined as follows:DEFINITION: For an open sentence p(x) and a set S, "! x S) (p(x))" (read "there is amique x in S such that p(x)") means:(3x S) (p(x)) and (Vu, vES) ([p(u) and p(v)] ⇒ u = v).a) Explain, in intuitive terms, how "(3! xment from S in the truth set of p(x).S) (p(x))" says that there is exactly one ele-

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is "3!", the existential quantifier foll DEFINITION: For an open sentence p(x) and a set S, "(! x S) (p(x))" (read "there is a nique x in S such that p(x)") means: (3x ES) (p(x)) and (Vu, vES) ([p(u) and p(v)] ⇒ u = v). a) Explain, in intuitive terms, how "(3! x S) (p(x))" says that there is exactly one ele- ment from S in the truth set of p(x).

is "3!", the existential quantifier foll DEFINITION: For an open sentence p(x) and a set S, "(! x S) (p(x))" (read "there is a nique x in S such that p(x)") means: (3x ES) (p(x)) and (Vu, vES) ([p(u) and p(v)] ⇒ u = v). a) Explain, in intuitive terms, how "(3! x S) (p(x))" says that there is exactly one ele- ment from S in the truth set of p(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 80E

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