if product and xor of ascii of strings together is used as key in map c++ will it be unique how to prove it

The uniqueness of a key in a map in C++ using the product and XOR of ASCII values of strings cannot be guaranteed. Here's why:

1. ASCII values: ASCII values are integers that represent characters. Each character has a unique ASCII value between 0 and 127 in the standard ASCII table.

2. Product of ASCII values: If you take the product of ASCII values of a string, it's not unique. For example, the strings "abc" and "cba" will have the same product because the order of multiplication doesn't matter.

3. XOR of ASCII values: XOR is a binary operation that gives the sum without carrying. If you take the XOR of ASCII values of a string, it's also not unique. For example, the strings "abc" and "bca" will have the same XOR value because XOR is commutative and associative.

4. Combination of product and XOR: Even if you combine the product and XOR of ASCII values, it's still not unique. The combination might reduce the chance of collision, but it doesn't eliminate it.

To prove it, you can simply find two different strings that result in the same product and XOR of ASCII values. For example, the strings "abc" and "cba" have the same product of ASCII values, and the strings "abc" and "bca" have the same XOR of ASCII values. Therefore, using the product and XOR of ASCII values as a key in a map in C++ is not guaranteed to be unique.