Question 1052740: Good morning ma'am/sir:
I need your help for the following problems on quantification.
Instructions: Let the universe of discourse in each case be the set of natural numbers.Determine the truth value. If true,prove it. If false,provide a counterexample.
1. For all x there exist y such that (x < y)
2. There exist x for all y such that (x < y)
3. There exist x for some y such that (x < y).
Please help me. Thank you!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The natural numbers are 1, 2, 3, ...
1. For all x there exist y such that (x < y) is TRUE,
because y=x+1 is a natural number, and x
2. There exist x for all y such that (x < y) is FALSE, because if Y=1, there is no natural number x such that x<1.
3. There exist x for some y such that (x < y) is TRUE, because for all natural numbers y except y=1, there is x=1, such that x
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