Provide further motivation for defining  to be true when p is false. We consider changing...

Provide further motivation for defining  to be true when p is false. We consider changing the truth table for when p is false. For the first change, we call the resulting operator imp1, and. for the second change, we call the resulting operator imp2. In both cases, we see dun pathologies result.

Define the truth table for imp2 by

(a) Show that

(b) Show that above equation remains true if we change the third row of imp2's truth table to F T F.