See the attachment for all questions.
18. Given: If you are wealthy, then you are a success.
You are wealthy or you are. healthy.
You are not healthy.
Let W represent: "You are wealthy." Let S represent: "You are a success." Let H represent: "You are healthy."
Prove: You are a success.
19. Given: The object is red or it is a pencil.
If it is a pencil, then it must contain carbon..
The object does not contain carbon.
Let R represent: Let P represent: Let C represent:
"The object is red." "It is a pencil."
"It contains carbon."
Prove: The object is red.
Please see the attachment
3. Modus Tollens (MT) from 1, 2
5. Disjunctive Syllogism (DS) from 3, 4
2. Decomposing a Conjunction (DC) from 1
4. DS from 2, 3
6. MT from 4, 5
The result is not correct. Here is a counter example
is false, is true, is false, is true. Then they satisfy all premises. But if false.
Some conditions are missing because the condition does not ...
The expert writes formula proofs and logic laws for proofs.