Question: for each of the following statements involving quantifies determine whether...
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.
- For all xeR, x2+ x >= 0
- For all xeZ there exists yeZ such that x2 + y2 is a perfect square.
- For all x,yeN, if x < y, then there exists ZeN such that x<z<y.