SOLUTION: Determine which, if any, of the three statements are equivalent. a) If Fido is our dog’s name, then Rex is not our dog’s name. b) It is false that Fido is our dog’s name and Rex

Algebra ->  Equations -> SOLUTION: Determine which, if any, of the three statements are equivalent. a) If Fido is our dog’s name, then Rex is not our dog’s name. b) It is false that Fido is our dog’s name and Rex       Log On


   

Question 1120041: Determine which, if any, of the three statements are equivalent.
a) If Fido is our dog’s name, then Rex is not our dog’s name.
b) It is false that Fido is our dog’s name and Rex is not our dog’s name.
c) Fido is not our dog’s name or Rex is our dog’s name.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let F represent the statement "Fido is our dog's name," and let R represent the statement "Rex is our dog's name."

The three statements to be evaluated are: (a) F -> ~R, (b) ~F & ~R, and (c) ~F v R.

Use a truth table. Equivalent statements will have identical truth tables:

   F   ~F   R   ~R   F -> ~R   ~F & ~R   ~F v R

   T    F   T    F      F         F         T
   T    F   F    T      T         F         F
   F    T   T    F      T         F         T
   F    T   F    T      T         T         T

None of the three statements to be evaluated have identical truth tables, therefore none of the three statements are equivalent.


John

My calculator said it, I believe it, that settles it