Is Rick Astley consistent in his song?

The question that most concerns me here is, is Rick Astley consistent in his song, "Never Gonna Give You Up"?  The way to prove that he is, is to start by assuming all his lyrics are true, and then see if there is any contradiction in holding them as all true simultaneously.  Let's see (there is a little license taken here with the lyrics):

Statement #1: Never gonna give you up and never gonna let you down.
Statement #2: Never gonna both run around and desert you.
Statement #3: If I'm never gonna make you cry then I'm never gonna let you down.
Statement #4: Never gonna give you up nor hurt you.

For those of you who know symbolic logic, this would go as follows:

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)

Assume they are all true:

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)
       T           T                               T                 T

Fill in for the last statement:

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)
       T            T                              T                 T      F

G and H must be false:

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)

 TF   T         T                              T                 T  F F F

D must be false:

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)

 TF   T  TF   T            F                 T        TF   T   F F F

R can be True

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)

 TF   T  TF   T  T   F  F                 T        TF   T   F F F

And C can be True

~G dot ~D / ~ (R dot D) / ~C horseshoe ~D / ~ (G v H)

 TF   T  TF   T  T   F  F    FT         T        TF   T   F F F

And there you have it - it is definitely possible that all these propositions can be true simultaneously.  

WE CAN TRUST RICK ASTLEY!!!

And you've been officially RickRolled!