Let x < 0, 0 < y < 1, z > 1. Which of the following may be false? Choose the correct choice: A) (x^2– z^2) has to be positive. B) yz can be less than one. C) xy can never be zero. D) (y^2– z^2) is always negative. E) None
Explanation :   Let's take any random value satisfying the given condition i.e x &lt; 0, 0 &lt; y &lt; 1, z &gt; 1.   Take x = -1, and z = 2   x2 - z2 -&gt; (-1)2 - (2)2 = -3 .   Take y= 0.1,   then , yz -&gt; (1/10)*2 = 1 /5 i.e less than 1.   According to the given condition, x and y both are non zero, so there product can't be zero.   Since, value of z will always be greater than 2 and y will always be less than 1, So, y2 - z2 will always result into a negative value.   Hence, only first option is false.   (x^2– z^2) has to be positive.nswer : (x^2– z^2) has to be positive.
<result>A</result>
Let x < 0, 0 < y < 1, z > 1. Which of the following may be false?