predicate truth trees 3 mp4
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Here's the last rule that we need
to deal with predicate truth trees
and it's a rule for when the main operator is a negation
of a quantified statement, so this is a negation of a universal
or a negation of an existential statement.
Here's what we do:
we push that tilde through and it only hops one place
it goes right to the other side of the quantifier
it doesn't go further in, it doesn't attach to anything in here
it just hops one place.
And as it does that, as it hops here or as it pushes through,
it always changes the quantifier.
If it's "X" it will become "EX," if it's "EX," it will become "X."
So let's do that now.
Change the quantifier, tilde goes right on the other side of the quantifier.
Everything else exactly the same as it was.
And with "EX," the quantifier becomes "X," the tilde moves
in one place, everything else stays exactly the same.
And now you are ready to use, in this case here,
the rule for "EX," take off the quantifier
replace with a brand new constant.
Same thing with this universal. Take off that
replace the "x's" with every constant that shows up.
And that's it!
And always remember to check those off.