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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. ►Full DISCRETE MATH Course Playlist:    • Discrete Math (Full Course: Sets, Log...   Other Course Playlists: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ►CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►CALCULUS III:    • Calculus III: Multivariable Calculus ...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   ***************************************************** YOUR TURN! Learning math requires more than just watching math videos, so make sure you reflect, ask questions, and do lots of practice problems! **************************************************** ►Follow me on Twitter:   / treforbazett   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett