I can't figure out if this statement is true or false, i said false

mr_coffee

This chapter is working with negations of Quantified statements.

True or False. All the occurrrences of the letter u in the title of this book are lower case. Justify your answer.

I said false, because they arn't being clear when they say "this" If even 1 book doesn't have a lowercase its false. But what is the method you would go about solving this?

I never took a negation of a non-if then statement. If its if then, its pretty easy:
~(Ax, if P(x) then Q(x)) equivlent too Ex such that P(x) and ~Q(x)
or

Ax in D, Q(x) equivlent Ex in D such that ~Q(x)

Note: A should be upside down, and E should be backwards.

THanks!

HallsofIvy

If this problem was in a chapter of your textbook, look at the title of your textbook!

mr_coffee

It was, the title of my text book is:

Susanna S. Epp
Discrete Mathematics with applications Third Editition

So is Susanna S. Epp part of the title? I think not, so it has to be false right?

0rthodontist

Are all unicorns green? In logic this translates to,
For all x, if x is a unicorn, x is green.
or more informally
If there is a unicorn, it is green.

There aren't any unicorns, so the antecedent of that implication is false. So all unicorns are green.

Does this help you?

mr_coffee

yes I believe so! Since the title of the book has no u's (they don't exist, like the unicorn), So All the occurrrences of the letter u in the title of this book are lower case.