Question

Class: Introduction to Logic

Write a natural deduction proof for the following deductive, valid argument.

1. (A > Z) & (B > Y)

2. (A > Z) > A / Z v Y

Answer #1

Write a proof of the following argument: "There is someone in
this class that likes escape rooms. Every in this class can solve
logic puzzles. Therefore, there is someone that likes escape rooms
and can solve logic puzzles."
Hint: Translate the English sentences into logic using the
domain "people" and apply rules of inference to prove why the
conclusion follows from the premises.

#1. Use propositional logic to prove the following
argument is valid.
If Alice gets the office position and works hard, then
she will get a bonus. If she gets a bonus, then she will go on a
trip. She did not go on a trip. Therefore, either she did not get
the office position or she did not work hard or she was late too
many times.
Define your propositions [5 points]:
O =
W =
B =
T =...

5) Use propositional logic to prove that the argument is
valid.
A’ Λ (B → A) → B’
1.____________ ____________
2.____________ ____________
3.____________ ____________

Consider the natural deduction proof given below. Using your
knowledge of the natural deduction proof method and the options
provided in the drop-down menus, fill in the blanks to identify the
missing information (premises, inferences, or justifications) that
completes the given application of the simplification (Simp)
rule.
1.(M ≡ O) • ~(S ⋁ G)
2.M
3.~(S ⋁ G) • (O ⊃ ~M)
4.~S/ ~(S ⋁ G)
5.~(S ⋁ G) _____________ Simp

Block copy, and paste, the argument into the window below, and
do a proof to prove that the argument is valid.
1. (s • z) • (p • x)
2. (s • x) ⊃ m
3. ~m v s : .
s

Block copy, and paste, the argument into the window below, and
do a proof to prove that the argument is valid.
1. (s • z) • (p • x)
2. (s • x) ⊃ m
3. ~m v s : .
s

5) Translate the following argument into symbolic form and then
use natural deduction (first 18 rules of inference) to derive the
conclusion of each argument. Do not use conditional proof or
indirect proof.
The Central Intelligence Agency (CIA) will lose its funding only
if the President thinks that it is wise and the Congress supports
the move. If either Congress supports the move or covert operations
run amok, then the CIA will have political problems. Therefore, if
the CIA will...

Use natural deduction to derive the conclusion in each
problem.
Use conditional proof or indirect proof as needed:
1.
(x)(Jx⊃∼Ga)
2.
(∃x)(Jx • Gc)
/ a ≠ c

Block copy, and paste, the argument into the window below, and
do a proof to prove that the argument is valid. This question is
worth 25 points.
1. r ⊃ ~q
2. p • r
3. x v q : . x

INSTRUCTIONS: Use natural deduction to derive
the conclusion in each problem.
Use conditional proof or indirect proof as needed:
1.
(x)[(Kx∨Nx)⊃(Ex •∼Rx)]
2.
(x)[(Kx∨Sx)⊃(Rx∨Hx)]
/ (x)[Kx⊃(Ex • Hx)]

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