not true
counterexample
5 > -6 ----> true
then 5^2 > (-6)^2 ??
25 > 36 ----> False
the statement is true only for positive values of x and y, so
it is "sometimes true"
If both x and y are integers and x > y,
then x^2 > y^2.
counterexample
5 > -6 ----> true
then 5^2 > (-6)^2 ??
25 > 36 ----> False
the statement is true only for positive values of x and y, so
it is "sometimes true"
The statement says that if both x and y are integers and x > y, then x^2 > y^2.
Let's consider an example to understand this statement.
Example:
Let x = 3 and y = 2.
In this case, x = 3 is greater than y = 2.
Now, let's calculate the squares of x and y:
x^2 = 3^2 = 9
y^2 = 2^2 = 4
From the example, we can observe that x^2 = 9 is indeed greater than y^2 = 4. Therefore, the statement "If both x and y are integers and x > y, then x^2 > y^2" is true in this example.
To generalize this, for any two integers x and y, where x > y, the statement will always hold true. This is because squaring both x and y will result in larger values for x^2 compared to y^2, given that x and y are positive integers.
Hence, we can conclude that the statement is true.