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

###### Question details

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 b^{2} = a.

- For all xe
**R**, x^{2}+ x >= 0 - For all xe
**Z**there exists yeZ such that x^{2}+ y^{2}is a perfect square. - For all x,ye
**N**, if x < y, then there exists ZeN such that x<z<y.