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Only if the negative sign is associated with an even root. In that case, the number is neither rational nor irrational, but is imaginary.
Statement 1 is true but totally unnecessary. As integer is always a rational and you do not need to convert it to a fraction to determine whether or not it is rational. A negative fraction is can be rational or irrational. The fact that it is negative is irrelevant to its rationality. An integer number over a zero denominator is not defined and so cannot be rational or irrational or anything. It just isn't.
No, it is always true.
That is not true.
Yes, since it can be written as a ratio of two integers: 19/5