Integral of f·g ≠ integral f · integral g [True or False]

[MiddleEast]

Homework Statement

True or False : Integral of f·g ≠ integral f · integral g

Relevant Equations

NA

My answer is False! I think must stated "in general," in the beginning of the statement. Cause this could be true if f or g = zero. There may be other cases also.
Is my answer right?

 

[DrClaude]

If integral of f·g ≠ integral f · integral g is false, then integral of f·g = integral f · integral g.

Thus this make sense?

 

[MiddleEast]

Hmmm. Good point! The issue here is that my point is "sometime true sometimes false" & your point "If it not true, then it is always false". huge difference between my point of view and yours! I believe it has something to do with "logical mathematics" if there is something called so.

The issue if you said it is true then I have my counter-example.

 

[Office_Shredder]

You obviously understand the point, and the answer at this stage is semantics over the implicit qualifier. I think it's a confusing question.

 

[PeroK]

There's no clear notation in mathematics for "not necessarily equal to". The best we can do is say something like, for example:

For functions $f$ and $g$ in general $f \circ g \ne g \circ f$. Even though there are cases where equality holds.

 

[mathwonk]

in my opinion, if the answer can only be true or false, that implies to me that the statement is universally quantified, so i would argue the correct answer should be false. since the statement is not explicitly quantified however, one could argue that it is poorly posed.