Question

For all integers a and b, if a < b then a² < b²?

Answer 1

Yes, for all integers a and b, if a < b, then a² < b².

Step-by-step explanation:

Yes, for all integers a and b, if a < b, then a² < b².

To prove this, we can consider different cases:

1. If both a and b are positive integers, then a² is less than b². For example, if a = 2 and b = 3, then a² = 4 and b² = 9.
2. If both a and b are negative integers, then a² is also less than b². For example, if a = -3 and b = -2, then a² = 9 and b² = 4.
3. If a is negative and b is positive, then a² is still less than b². For example, if a = -2 and b = 3, then a² = 4 and b² = 9.

Therefore, we can conclude that if a < b, then a² < b².