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  3. for each of the following statements involving quantifies determine whether...

Question: for each of the following statements involving quantifies determine whether...

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For each of the following statements involving quantifies, determine whether it is True or False and explain.

R denotes the set of real numbers. N denotes the set of natural numbers (0,1,2,3,4…). Z denotes the set of integers (0, +/-1, +/-2. An integer is called a perfect square if there is another integer b such that b2 = a.

  1. For all xeR, x2+ x >= 0
  2. For all xeZ there exists yeZ such that x2 + y2 is a perfect square.
  3. For all x,yeN, if x < y, then there exists ZeN such that x<z<y.
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