43 Proof by Natural Deduction Propositional Logic Use a dir

43. Proof by Natural Deduction – Propositional Logic. Use a direct proof to show that the following argument is valid.

Premise 1: E v (M •U)

Premise 2: ~E

Conclusion: ~(E v ~M)

Solution

Since ~E is true, this implies E is false . ----(1)

Using deduction (1) from Premise 2 in Premise 1:
(E) V (M.U) is true but E is false thus M.U is true.
That implies M is true and U is true -----(2)

Using deduction (1) and deduction (2)
~E /\\ M is true
Using de-morgan\'s law
~(E V ~M) is true
Hence proved