Determine if the following statement is true. For any numbers a and b, if a > B, then a2 > b2. Give a justification for your response.
I'm so confused on this one too. I'm trying to find help in my book but cannot understand.
Pick two different numbers. Let one be A and let the other be B. Keep trying different numbers (i.e. positives, negatives, and even zero). Are there any examples where this statement is false? I do not see any. The statement is true.
Can you tell me how you got this answer? I don't understand the example. I'm sorry. I'm not good at this.
To determine if the statement is true, we need to apply logical reasoning and understand the mathematical principles involved.
The statement given is: "For any numbers a and b, if a > b, then a^2 > b^2."
To justify the response, we can break it down and apply a logical reasoning process.
1. Assume that a and b are any two numbers. It is important to remember that this statement applies to all numbers and not just specific examples.
2. Now, let's assume that a > b. This means that the number a is greater than the number b.
3. To determine if the statement is true, we need to check if a^2 > b^2. This means we need to compare the squares of both a and b.
4. Square both sides of the inequality from the assumption a > b. We get (a^2) > (b^2).
5. Comparing a^2 and b^2, we can conclude that if a > b, then a^2 > b^2.
So, the statement "For any numbers a and b, if a > b, then a^2 > b^2" is true. It is supported by the logical reasoning that when a number is greater than another number, their squares will follow the same inequality relationship.