nested derivation worksheet questions help
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Humanities
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EXAM 4
JESSE FITTS
Directions: If you use a word processor, and aren’t handwriting the test (which I
recommend) use this symbol—
|
—(usually the same key as the slash) for the side of the box. For each nested
derivation, you’ll be adding more and more | symbols to represent the scope of
each. For the line annotations, you can just tab over from the formula—no need to
make sure all the annotations line up. To cancel a Show line, put an X after that
Show line (or, if you’re inclined, use strikethrough text, but an X will suffice). An
example (not in predicate logic as this exam is) should make this clear:
1.
2.
3.
4.
5.
6.
(P ∨ Q) → R
Pr
SHOW X: Q → R
CD
|Q
As
| SHOW X: R
DD
|| P ∨ Q
3, ∨I
|| R
1, 5, → O
If you’re using Word or something similar, it’ll probably try to force you into
the number environment, where it automatically adds a number when you press
‘enter.’ That’s fine—the only thing that matters is that you use | for the boxes
and that you cancel your Show lines.
Use the same symbols you used on your other exams (–> for →, etc.)
1. Question 1
∀x(∼Gx ∨ Sx)/∀xGx → ∀xSx
2. Question 2
∀x(Gx → ∼F x); ∀x(Hx → Gx)/∼∃x(Hx&F x)
3. Questions 3
∃x(F x&Gx); ∼∃x(F x&∼Hx)/∃x(Hx&Gx)
1
4. Questions 4
∃x(F x ∨ Gx) → ∀x∼Hx/∀x[(F x ∨ Gx) → ∼∃yHy]
5. Questions 5
∃x∼∃y ∼Rxy/∀x∃yRyx
6. Questions 6
∃x[F x&∀y(Hy → ∼Rxy)]/∀x[Hx → ∃y(F y&∼Ryx)]
2
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