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Jimmy84
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Homework Statement
prove that if a is less than zero , and if b is less than zero then ab is greater than zero.
I have been having troubles with this problem.
thanks.
Office_Shredder said:What have you tried so far? Do you know what axioms for positivity you can use?
The statement "a,b<0" means that both a and b are negative numbers.
The symbol "$\implies$" is a logical symbol that means "implies" or "if...then". In this context, it is used to show that if a and b are both negative, then the product of a and b will be positive.
This statement can be proven using the rules of algebra and properties of real numbers. We can start with the assumption that a and b are both negative, and then use algebraic manipulations to show that the product of a and b is indeed positive.
Proving this statement is important because it helps to understand the relationship between negative numbers and their products. It also helps to strengthen our understanding of basic algebraic principles and logical reasoning.
Yes, this statement can be generalized to include any number of negative variables. The statement would be: "If all variables are negative, then the product of those variables will be positive." This can also be proven using similar algebraic manipulations.