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Write formal proofs/Logic laws for proofs

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.

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Solution Preview

Please see the attachment

Problem #3
1. Premise
2. Premise
3. Modus Tollens (MT) from 1, 2
4. Premise
5. Disjunctive Syllogism (DS) from 3, 4

Problem #4
1. Premise
2. Decomposing a Conjunction (DC) from 1
3. Premise
4. DS from 2, 3
5. Premise
6. MT from 4, 5

Problem #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.

Problem #6
Some conditions are missing because the condition does not ...

Solution Summary

The expert writes formula proofs and logic laws for proofs.