Question

Disprove, by finding a suitable counter example, the statement x²> y² for all x>y.

Answer 1

Q: Disprove :
${x}^{2} > {y}^{2} \forall x > y$

Solution :
Let x = -1 , y = -2
Then,$x > y$
But,
${x}^{2} = {( - 1)}^{2} = 1 \\ {y}^{2} = {( - 2) }^{2} = 4$
=> $y^2 > x ^2$
Hence,
Disproved

Answer 2

Hi ,

Let x = 2 , y = -3

x > y

x² > y²

2² > ( - 3 )²

4 > 9 ( False )

Therefore ,

for all x > y , x² > y² is not true .

I hope this helps you.

: )