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How do you construct a truth table for p arrow q and p arrow -q. Also do truth tables differ depending on the statement?
Wiki User
∙ 15y ago
Statements mean nothing to the validity of truth tables. However p and q must be statements - something that can be declared true or false. Example: a statement could be "There are clouds in the sky over my head right now." A statement could not be "A cloudy day is dreary" -- that is subjective (maybe true to you but not necessarily to me).
That said the truth tables look at comparing all possible combinations of truth values for both statements: p could be true and q could be true, or p could be true and q could be false, or p could be false and q could be true, or p could be false and q could be false.
Then you can look at the if p then q (p arrow q) truth values. Consider the If-then statements most teens hear: If you clean your room, then you can take the car out on Friday. The Parent is considered lying if they don't let you take the car out even though you cleaned your room. If you don't clean your room, the "then" part of the conditional statement does not matter -- logically then if p is not true, the conditional is considered true regardless of the value of q.
table looks like
p | q | p -> q
T | T | T (you clean your room and you do get to take the car on Friday)
T | F | F (you clean your room and you don't get to take the car on Friday)
F | T | T (you don't clean your room - the rest doesn't matter)
F | F | T
The table for p begets not q is almost the same. Start with the same two first columns, add a column for not q (~q); then add a column to evaluate the conditional. Only this time your parent said something like "If you fail your Geometry quiz, then you can NOT go to the party on Saturday". They only lied to you if you failed your quiz and they still let you go to the party.
Wiki User
∙ 15y ago
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