Question 1102473: For each statement,state whether it is always,sometimes,or never true, and briefly justify each answer:
N) If 𝑞 ∈ N, then there exists a number 𝑝 ∈ N such that 𝑝2 = 𝑞.
Z) If 𝑞 ∈ Z, then there exists a number 𝑝 ∈ Z such that 𝑝2 = 𝑞.
Q) If 𝑞 ∈ Q, then there exists a number 𝑝 ∈ Q such that 𝑝2 = 𝑞.
R) If 𝑞 ∈ R, then there exists a number 𝑝 ∈ R such that 𝑝2 = 𝑞.
C) If 𝑞 ∈ C, then there exists a number 𝑝 ∈ C such that 𝑝2 = 𝑞.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! N)  true.
 = the set of natural numbers, or counting numbers, {1, 2, 2, ...}
For  , there is  such that  ,
but for  , if  , then  does not belong to set N.
Z) true.
 = the set of integers
For , there is such that ,
but for , if , then does not belong to set Z,
and for integer  there is neither integer, nor rational, nor real number  such that  .
Q) true.
 = the set of rational numbers.
All the examples above still work the same way,
so it is still sometimes true, and sometimes not true.
No need to look for more examples.
R) true.
 = the set of real numbers.
For any non-negative real number  ,
there are always two real numbers  , such that  .
However, for negative numbers, that is not true.
For  , there is no real number such that  .
C)  true.
 = the set of complex numbers.
For every complex number  there are always two complex numbers and  , such that  .
Any complex number can be written as  ,
with  being a non-negative real number,  ,
and  being an angle with  ,
For complex number  , .
For  , too.
and  p=
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