PLEASE PROVIDE THOROUGH PROOFS Write the following propositions with the appropr

Question

PLEASE PROVIDE THOROUGH PROOFS

Write the following propositions with the appropriate universal and existential quantifiers and sentential connectives. Then write their negations. Do not use phrases such as "it is not the case that" and "it is not true that," etc. Let f be a function whose domain and codomain arc R. Write the following definition for continuity of functions using the appropriate universal and existential quantifiers and sentential connectives: "For every and for every , if , then there exists a such that delta > 0 and that the following implication holds: for every , then |f(x)-f(y)|

Explanation / Answer

(there is some e>0)(for all d > 0)(there is some x with |x-a| < d and |f(x) - f(a)| >= e )

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