There are tons of women who enjoy the damsel in distress trope and think it’s harmless fun.
There are also tons of women who think it perpetuates sexist stereotypes against women.
Both groups of women’s opinions are equally valid.
Does this not prove that the statement is independent?
Real life is not math. To get more pointy headed about it, math has been described as the one place where classical logic actually works. In other contexts, you can’t really chain inferences more than one or two deep, can’t really use the law of excluded middle. The blue-eyed islanders’ problem can only be seen as a clever math puzzle rather than a question about a hypothetical reality, etc.
For those who don’t understand the above: you’re not missing much, so don’t worry.
Tell that to graph theory.