# Truth Table #1

 P Q ~P ~Q P  = ~Q (P = ~Q) = (Q = ~P) Q = ~P P & Q (P & Q) = (P or Q) P or Q P = Q (P = Q) = (~P = ~Q) ~P = ~Q P =  ~P Q = ~Q TRUE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE 1 TRUE FALSE FALSE TRUE TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE 2 FALSE TRUE TRUE FALSE TRUE TRUE TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE 3 FALSE FALSE TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE 4 A B C D E F G H I J K L M N O

 Statement P: You're good. Statement Q: You're evil.

(P = ~Q) = (Q = ~P) -- Remember that tautologies are always true!

P & Q, Row #1 -- Got moral confusion? This is the cell with the morality paradox! It commits the Black-and-White Fallacy. In this row, Statement P is NOT coincidental to the negation of Statement Q, and vice versa; in fact, the 2 biconditionals are FALSE. However, Column F is a tautology, and this tautology says that when Columns E & G are FALSE, someone could possibly be good & evil at the same time! But not all the time according to Cell H4. Therefore, good & evil are not just antonyms, but also contraries of each other, which can make a conjunction logically TRUE; but they're NOT contradictories of each other; contradictories can't equal each other!

P = Q, Rows #1 & #4 -- Still morally confused? Since both Statements P & Q are TRUE in this row, their negations are FALSE, which makes this biconditional statement logically TRUE in this row; vice versa happens on the last row, so it's also TRUE in that row. Contraries can also make biconditional statements logically TRUE. The exact same thing occurs with their negations. (Column M shows that) However, it's still TRUE that good & evil are opposites(or antonyms) because of their definitions. Opposites can be based on something relative, like temperature; I also could have picked hot & cold as the antonyms between Statements P & Q. (In other words, [hot = cold] can also be TRUE at least 50% of the time!) People can say that something is hot, but it can still be relatively cold compared to something else! The same is TRUE for morality, as in kindness vs. cruelty!

P = Q, Rows #2 & #3 -- When [good = not evil] & [evil = not good] are TRUE as usual, good & evil are more understandable, obvious opposites. (Or antonyms) However, [good = not good] & [evil = not evil] are both contradictions since contradictories can't equal each other. (Examine Columns N & O) Contradictions are compound statements that are always FALSE!

(P = Q) = (~P = ~Q) -- This statement is also a tautology! But even with relativity, all of this still makes some sense, despite a fallacy!

# Truth Table #2

 R P Q R = (P & Q) (R = (P & Q)) = (R = (P = Q)) R = (P = Q) TRUE TRUE TRUE TRUE TRUE TRUE 1 TRUE TRUE FALSE FALSE TRUE FALSE 2 TRUE FALSE TRUE FALSE TRUE FALSE 3 TRUE FALSE FALSE FALSE FALSE TRUE 4 FALSE TRUE TRUE FALSE TRUE FALSE 5 FALSE TRUE FALSE TRUE TRUE TRUE 6 FALSE FALSE TRUE TRUE TRUE TRUE 7 FALSE FALSE FALSE TRUE FALSE FALSE 8 A B C D E F

 Statement P: You're good. Statement Q: You're evil. Statement R: You're morally confused!

R = (P & Q) -- This is the statement that says being morally confused is the same as being good & evil at the same time!

(R = (P = Q)) -- This statement suggests when moral confusion is TRUE if morality is relative.

(R = (P & Q)) = (R = (P = Q)) -- Since this compound statement isn't a tautology, the 2 compound statements within it are NOT logically equivalent. (Their truth values are different in Rows #4 & #8) However, the truth of each one is as likely as the other.

P.S.: Some of these compound statements are logically equivalent! Do you know which ones they are?

P.P.S.: Remember that "true" can also mean "not falsified" or "proven not to be false". That's an extremely important fact to remember about logic!