Hello, I need help writing proofs for a logic and moral reasoning philosophy class. The proofs are for: 1. Premises: q -> (q &~ q) Conclusion: ~q 2. Premises: k & l

Hello,

I need help writing proofs for a logic and moral reasoning philosophy class.

The proofs are for:

1. Premises: q -> (q &~ q)

            Conclusion: ~q

2. Premises: k & l

            Conclusion: (k - > l) & (l -> k)

3. Premises: p & (q V r), p -> ~r

            Conclusion: q V e

4. Premises: ~(p -> q)

            Conclusion: ~q

5. Premises: (a V b) & (c V d), a -> (e -> (c &d)), c <-> ~d

            Conclusion: e -> b