# 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.

https://brainmass.com/math/linear-algebra/write-formal-proofs-logic-laws-proofs-558104

#### 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.