Negating Universal and Existential Quantifiers

How do you negate a statement with "for all" or "there exists" in them? "For all" and "There Exists". For all, and There Exists are called quantifiers and they turn a predicate P(x) into a statement "For All x, P(x)" that is true or false. When you negate these types of statements the For All and There Exist symbols change places, the the negation factors through. That is "NOT For All x, P(x)" becomes "There Exists an x such that, NOT P(x)".

Learning Objectives:
1) symbolically negate statements with universal and existential quantifiers
2) Given a sentence, interpret it symbolically and then write a sentence for the negation.

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