Put TTTTFFFF under each H, TTFFTTFF under each E,
and TFTFTFTF under each D.
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
T T T T T T T
T T F T T T F
T F T T F T T
T F F T F T F
F T T F T F T
F T F F T F F
F F T F F F T
F F F F F F F
Under each ~, put the opposite of what follows it under it
and erase what was next to it:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
F T T T F T F
F T F T F T T
F F T T T T F
F F F T T T T
T T T F F F F
T T F F F F T
T F T F T F F
T F F F T F T
Under each •, put T only if the • is between two T's,
and put F otherwise, and erase the two that the • is
between:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
F T F F
F F F T
F F T F
F F T T
T T F F
T F F F
T F F F
T F F F
Under each ∨, put F only if the ∨ is between two F's,
and put T otherwise, and erase the two that the ∨ is
between:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
T F
F T
F T
F T
T F
T F
T F
T F
Under the ≡, put T only if the ≡ is between two that
are the same, and F if the ≡ is between two that are
not the same. and erase the two that the ≡ is
between:
[∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)]
F
F
F
F
F
F
F
F
Since the final column has all F's the proposition is a
contradiction, which means that it is never true!
Edwin
