Philosophy homework help

Question

The image displays three logical premises and a fourth line to be completed using the "Dist" (Distribution) rule.

Here are the premises:

1. (F∨N)⊃(K⋅D)
2. (H⋅Z)∨(H⋅W)
3. (P⊃H)∨(P⊃N)

Answer 1

Hello, To apply the “Dist” (Distribution) rule in logic, you’re distributing a shared element across a disjunction or conjunction. This is often used with statements like:

1. A \cdot (B \vee C) \equiv (A \cdot B) \vee (A \cdot C)
2. A \vee (B \cdot C) \equiv (A \vee B) \cdot (A \vee C)

In your case, line 2 is the one eligible for Distribution:

2. (H \cdot Z) \vee (H \cdot W)

This fits the pattern (A \cdot B) \vee (A \cdot C), which can be factored as:

H \cdot (Z \vee W)

So applying the Dist rule to line 2, the fourth line would be:

4. H \cdot (Z \vee W) (from 2 by Dist)