quantifiers - Quantiers Professor Sormani A supplement for...

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Quantifiers Professor Sormani A supplement for MAT175 Quantifiers are special symbols that are used to make it easier to think about math- ematical statements. There are three quantifiers: means “for all” “for every” means “there exists” “there is a” ! means “there exists unique” or “there is only one” The following statements are true. Why? x [0 , 1] , sin ( x ) is well defined . and x [ - 1 , 1] such that 1 /x is undefined . and f : [0 , 1] [0 , 3] has an inverse if y [0 , 3] ! x [0 , 1] such that f ( x ) = y. Now write true and false next to the following statements after translating them. The answers are below so you can check each answer before continuing. 1) x [0 , π/ 2] such that sin ( x ) = 1 . 2) x [0 , π/ 4] such that sin ( x ) = 1 . 3) ! x
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