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Make the truth table of the proposition ¬q→[(pΛq)V~p]?

1 Answer
Apr 1, 2018

Answer:

See below.

Explanation:

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" "|#