# Mixed Quantifers confusion! Descrete Math

by mr_coffee
Tags: confusion, descrete, math, mixed, quantifers
 P: 1,629 THe directions say< indicate which fo the following statements are true and which are false, Justify your answers as best you can. Here is the question: $$\exists$$ x $$\in$$ R such that $$\forall$$ $$\in$$ R, x = y + 1. I wrote the following: There exists a real number x such that given any real number y the property x=y+1 will be true. True. y = x-1. Then y is a real number, and y + 1 = (x-1)+1 = x. I really don't know if i did this right or not but there was an example but slighty different and the book had the following: $$\forall$$ x $$\in$$ Z, $$\exists$$ y $$\in$$ Z such that x = y + 1. There answer was: Given any integer, there is an integer such that tthe first inteer is one more than the second integer. this is true. Given any integer x, take y = x-1. Then y is an integer, and y + 1 = (x-1) + 1 = x. I'm really confused on how to go about tackling these problems. Any help would be great! thanks!
 HW Helper P: 2,567 For the first one, there needs to be a single x that works for all y. Note how this is different from the second one.
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P: 39,538
 Quote by mr_coffee THe directions say< indicate which fo the following statements are true and which are false, Justify your answers as best you can. Here is the question: $$\exists$$ x $$\in$$ R such that $$\forall$$ $$\in$$ R, x = y + 1.
Doesn't make sense. Did you mean $$\for all y[/itex] ?? If you meant [tex]\forall y$$ then y= x-1 works, doesn't it?

 I wrote the following: There exists a real number x such that given any real number y the property x=y+1 will be true. True. y = x-1. Then y is a real number, and y + 1 = (x-1)+1 = x. I really don't know if i did this right or not but there was an example but slighty different and the book had the following: $$\forall$$ x $$\in$$ Z, $$\exists$$ y $$\in$$ Z such that x = y + 1.
What is true in Z (set of all integers) is not necessarily true in R (set of all real numbers) but the difference is usually a matter of multiplication or division, not addition.