Question

Disprove, by finding a suitable counter example, the statement 

x² > y² for all x > y

Answer 1

If x = – 8 and y = – 10 

Here x > y 

x² = (- 8)² = 64 and y² = (- 10)² = 100 

But x² > y² is false here. [ ∵ 64 < 100] 

(This can be proved for any set of negative numbers or a negative number and a positive number)