I am having a lot of trouble with word problem questions. If someone could help me that would be great. If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!
8. (6 pts) Construct a truth table for (qp) q
Symbols copied as squares so: 1st square is a ~ , 2nd square is /\(v reversed), 3rd square is arrow pointing to right, 4th square is ~
We use all these
negation rules:
~T = F
~F = T
conjunction rules:
T/\T = T
T/\F = F
F/\T = F
F/\F = F
conditional rules:
T->T = T
T->F = F
F->T = T
F->F = F
(~q/\p) -> ~q
List all the "building blocks" of that. They are
p
q
~q
~q/\p
and end with the whole expression (~q/\p)->~q
Put these across in a table for the 4 possible cases:
p q ~q ~q/\p (~q/\p)->~q
case 1 T T
case 2 T F
case 3 F T
case 4 F F
Use the negation rules and what's under q to
fill in the list under ~q
p q ~q ~q/\p (~q/\p)->~q
case 1 T T F
case 2 T F T
case 3 F T F
case 4 F F T
Use the conjunction rules and what's under ~q and under p to
fill in the list under ~q/\p
p q ~q ~q/\p (~q/\p)->~q
case 1 T T F F
case 2 T F T T
case 3 F T F F
case 4 F F T F
Finally use the conditional rules and what's under
~q/\p and under ~q to fill in the last list:
p q ~q ~q/\p (~q/\p)->~q
case 1 T T F F T
case 2 T F T T T
case 3 F T F F T
case 4 F F T F T
Edwin