Assuming a is a non zero integer, which of the following statements is never true...
1. a > -a
2. a < -a
3. [a] = -a
4. [a] = - [a]
any explanation is welcome!
Assuming a is a non zero integer, which of the following statements is never true...
1 is true with $\displaystyle a=1$ and 2 is true with $\displaystyle a=-1$, also 3 is true with $\displaystyle a=-1$, I think the answer is 4
Because if $\displaystyle a$ is non-zero then $\displaystyle |a|\neq0$ too.
Question. Does $\displaystyle [a]$ denotes the lowest or greatest integer function? If so it is not meaningful since $\displaystyle [a]=a$ holds ($\displaystyle a$ is an integer).
But it would be nice to consider this question with real $\displaystyle a\neq0$.
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 question asked was "which of the answers are NEVER true".
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".