Question

Fill in the reasons in the following proof sequence. Make sure you indicate which step(s) each derivation rule refers to. Statements Reasons 1. (p^q)->r given 2. !(p^q)vr 3. (!pv!q)vr 4. !pv(!qvr) 5. p->(!qvr)

Answer 1

By applying the implication rule and the associative law, we can fill in the steps with the correct reasoning and derive the requested statement.

Step-by-step explanation:

1. !(p^q)->r (given)
2. !(p^q)v!r (Implication rule on step 1)
3. (!p v !q)v!r (De Morgan's law on step 2)
4. !pv(!qvr) (Associative law on step 3)
5. p->(!qvr) (Implication rule on step 4)