Zarrolou wrote:
Is x negative?
(i) x^2 is a positive number
x^2>0, so x\neq{0}, not sufficient to say that it is negative.
(ii) x * |y| is not a positive number
x*|y|\leq{0}, so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.
1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example 2*0\leq{0} this respects both conditions and x is positive, or -2*0\leq{0} here x is negative.
Not sufficient
E
(i) x^2 is a positive number
x^2>0, so x\neq{0}, not sufficient to say that it is negative.
(ii) x * |y| is not a positive number
x*|y|\leq{0}, so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.
1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example 2*0\leq{0} this respects both conditions and x is positive, or -2*0\leq{0} here x is negative.
Not sufficient
E
Hi Zarrolou,
I thought mod of Zero was illegal.
in (ii) x could be zero. But together we know x cannot be zero hence negative.