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welcome to the introduction to proofs video for negation my name is Professor Michael by the end of this video you should be able to create the negation of an English statement you should be able to formally negate a mathematical statement involving and not and if then you should be able to formally negate a mathematical statement involving multiple quantifiers our motivation is that taking the negation of a mathematical statement is the formal way of taking its opposite and its opposite is not well-defined itamp;#39;s itamp;#39;s vague imprecise but weamp;#39;re going to come up with formal ways of doing that this will allow us to transfer from a statement to its opposite and back again while we proceed through these slides and through this video itamp;#39;s useful for your intuition to think about if someone said a statement R to you what would you need to know to make sure that theyamp;#39;re lying so this isnamp;#39;t what weamp;#39;ll use for the rest of playing around with