If the steak is well done, it’s overcooked. If the steak is overcooked, the fire alarm will go off. Either the batteries have been changed or the fire alarm will not go off. The batteries have only been changed if the ladder is in the room. The ladder is not in the room. Conclude that the steak is not well done.   These premises don’t make sense in the real world. Why?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Inference 

Please break down into symbolic notation. See the example picture I provided. The answer should look similar to that. Also, include (for example, Premise 4, modus ponens next to the steps).

This question is in three parts.

Given the premises:

      1. If the steak is well done, it’s overcooked.
      2. If the steak is overcooked, the fire alarm will go off.
      3. Either the batteries have been changed or the fire alarm will not go off.
      4. The batteries have only been changed if the ladder is in the room.
      5. The ladder is not in the room.

Conclude that the steak is not well done.

 

These premises don’t make sense in the real world. Why?

 

How can you change the premises so that they make sense in the real world? (They don’t have to end up perfectly correct, but they need to avoid the obvious problems you uncover in part B.)

 

Breaking down into symbolic notation:
p: fish can fly
q: birds can swim
r: squirrels can talk
s: capybaras can write
Then we have premises:
1. p q
2.
qr
3. (q^r) → s
4. P
P
: (1) q
7
Premise 4
Premise 1, modus ponens
Premise 2, modus ponens
q^r (1), conjunction
modus ponens
S
Transcribed Image Text:Breaking down into symbolic notation: p: fish can fly q: birds can swim r: squirrels can talk s: capybaras can write Then we have premises: 1. p q 2. qr 3. (q^r) → s 4. P P : (1) q 7 Premise 4 Premise 1, modus ponens Premise 2, modus ponens q^r (1), conjunction modus ponens S
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