Question

Use an ordinary proof (not conditional or indirect proof):1.

∼N⊃ (∼R⊃ C) 2. R⊃ N 3.∼C / N

Answer 1

ANSWER:

Given that,

[~N->(~R->C)] ^ [R->N] ^ ~C

Using rule of material implication

=> [Nv(~R->C)] ^ [~RvN] ^ ~C

=> [Nv(RvC)] ^ [~RvN] ^ ~C

Using associative law and commutative law

=> [(RvN)vC] ^ [~RvN] ^ ~C

Using distributive law

=> [[(RvN) ^ (~RvN)] v [C ^ (~RvN)]] ^ ~C

Using rule of resolution

=> [(NvN)] v [C ^ (~RvN)]] ^ ~C

Using rule of disjunctive simplification

=> N v [C ^ (~RvN)]] ^ ~C

Using rule of simplification

=> N