Given: #not p -> [(p ^^ q)vv ~p]#

Logic operators:#" not p:" not p, ~ p; " and:" ^^ ; or:vv#

Logic Tables, negation:

#ul(|" "p|" "q|" "~p|" "~q|)#

#" "T|" "T|" "F|" "F|#

#" "T|" "F|" "F|" "T|#

#" "F|" "T|" "T|" "F|#

#" "F|" "F|" "T|" "T|#

Logic Tables, and & or:

#ul(|" "p|" "q|" "p^^q" "|" "qvvq" "|)#

#|" "T|" "T|" "T" "|" "T" "|#

#|" "T|" "F|" "F" "|" "T" "|#

#|" "F|" "T|" "F" "|" "T" "|#

#|" "F|" "F|" "F" "|" "F" "|#

Logic Tables, if then:

#ul(|" "p|" "q|" "p->q" "|)#

#|" "T|" "T|" "T" "|#

#|" "T|" "F|" "F" "|#

#|" "F|" "T|" "T" "|#

#|" "F|" "F|" "T" "|#

Given Logic proposition part 1:

#ul(|" "p^^q" "|" "~p" "|" "(p^^q)vv~p|)#

#|" "T" "|" " F " "|" "T" "|#

#|" "F" "|" " F " "|" "F" "|#

#|" "F" "|" " T " "|" "T" "|#

#|" "F" "|" " T " "|" "T" "|#

Given Logic proposition part 2:

#ul(|" "~q" "|" "(p^^q)vv~p|" "~q->(p^^q)vv~p|)#

#|" " F " "|" "T" "|" "T" "|#

#|" " T " "|" "F" "|" "F" "|#

#|" " F " "|" "T" "|" "T" "|#

#|" " T " "|" "T" "|" "T" "|#