daveyinaz said:Typically you would want to show that both inclusions are true...but in this case...is the element [tex]((a,b),c) = (a,(b,c))[/tex] ?
mbcsantin said:Yes, they're equal. It's called the Associative Property of Multiplication.
The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping:
(a . b) . c = a . (b . c)
To prove a statement, you must provide logical reasoning and evidence that supports the statement. This can include using mathematical equations, logical deductions, or empirical data to support your argument.
A counterexample is an example or situation that contradicts a given statement or hypothesis. It disproves the statement by providing evidence that goes against it.
To find a counterexample, you must look for a specific example or situation that goes against the given statement. This can involve trying different values or combinations of variables, or considering different scenarios that could disprove the statement.
Yes, any statement can be either proved or disproved by providing evidence or a counterexample. However, some statements may be more difficult to prove or disprove than others, and it may require more complex reasoning or evidence.
Proving or finding counterexamples is important in order to ensure that a statement or hypothesis is true and accurate. It also allows for further exploration and understanding of a concept or idea, as well as identifying potential flaws or exceptions to a statement.