I need help with this proof for my philosophy class. This proof is supposed to be done via indirect proof or conditional proof, so it is supposed to use AIP and IP or ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be precise and the assignment is due tonight, so I would like it done before tonight please!

This is the key:
The * = dot
The > = horseshoe
The v = wedge
The ≡ = triple bar
The ~ = tilde
The statement after the / (slash) is the conclusion that I need.
The problem is:
1. Y > [(S v M) > (E * K)]
2. D > [( K v Q) > (V * ~M)]
/ (Y * D) > ~ M

To prove the conclusion "(Y * D) > ~M" using indirect proof (IP), we assume the opposite of the conclusion and derive a contradiction. Here are the steps to follow:

1. Assume the negation of the conclusion: ~(Y * D) v ~M
2. Apply De Morgan's Law to the negated conjunction ~(Y * D): (~Y v ~D) v ~M
3. Use the Associative Law to rearrange the parentheses: ~Y v (~D v ~M)
4. According to the second premise (2), we have: D > [(K v Q) > (V * ~M)]
5. Apply the conditional elimination (→E) to premise 4: D > (K v Q) > (V * ~M)
6. Since ~D appears in our derived statement, use disjunction introduction (vI) to introduce ~D v P, where P can be any statement.
7. Now we have two cases to consider:
a) Case 1: Assume ~Y, and derive a contradiction.
b) Case 2: Assume ~D, and derive a contradiction.

Let's focus on Case 1: ~Y
8. Apply the conditional elimination (→E) to premise 1: Y > [(S v M) > (E * K)]
9. Assume S v M, and derive (E * K).
10. At this point, ~(Y * D) v ~M has been converted to ~D v ~M due to the assumption ~Y.
11. To derive a contradiction, assume ~M and derive a contradiction using disjunction elimination (vE) on ~D v ~M.
12. This contradiction proves ~M.

Now, let's examine Case 2: ~D
13. Use disjunction introduction (vI) to introduce Y v P, where P can be any statement.
14. Assume Y and derive a contradiction following a similar process as in Case 1.
15. This contradiction proves ~M.

By deriving a contradiction in both cases, we can conclude ~M, which contradicts the assumption ~(Y * D) v ~M made at the beginning.

Therefore, the original statement (Y * D) > ~M holds true according to the rules of indirect proof (IP).