If a and b are any real numbers such that 0<a<1<b, which of the following must be true ov the value ab??
The prob. is incomplete.
To determine the relationship between the value of ab, given 0 < a < 1 < b, we can analyze the given inequality conditions carefully.
Let's consider the possible scenarios with different values of a and b:
1. Consider a = 0.5 and b = 2:
In this case, ab = 0.5 * 2 = 1. The value of ab is greater than 1.
2. Consider a = 0.5 and b = 1.5:
In this case, ab = 0.5 * 1.5 = 0.75. The value of ab is less than 1.
3. Consider a = 0.1 and b = 2:
In this case, ab = 0.1 * 2 = 0.2. The value of ab is less than 1.
Based on these examples, we can see that the value of ab can vary and is not restricted to any specific range or comparison. Therefore, we cannot determine any absolute relationship between the value of ab and the given conditions 0 < a < 1 < b.
Hence, none of the options provided can be guaranteed to be true for the value of ab.