So, are you saying that all four answers are false? Could there be more than one false answer?
1 is true with and 2 is true with , also 3 is true with , I think the answer is 4
Because if is non-zero then too.
Question. Does denotes the lowest or greatest integer function? If so it is not meaningful since holds ( is an integer).
But it would be nice to consider this question with real .
In this case, the solution is 3.
Non of the answers are true
if a is not 0 ,it can be positive or nagative ,
check it with one positive for example 3,
then check it with negative for example -3
if these to numbers are not correct for any of the answer,any non ziro integer will act the same
The first, a> -a, is true whenever a is positive and so is not "never true".
The second, a< -a, is true whenever a is negative.
The third and fourth, |a|= -a and |a|= -|a| are true for a= 0.
NONE of the statments is "NEVER true".