This is the process I did, but I’m not sure if the procedure is correct:
P | Q | ?
F | F | F
F | T | T
T | F | T
T | T | F
(¬P ∧ Q) ∨ (P ∧ ¬Q)
=> ((¬P ∧ Q) ∨ P) ∧ ((¬P ∧ Q) ∨ ¬Q)
=> (P ∨ Q) ∧ (¬P ∨ ¬Q)
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The formula must be $P \lor Q$... – Mauro ALLEGRANZA Jan 11 '21 at 12:27
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1But a general procedure is: consider the rows in which the table outputs T and write a disjunct corresponding to each row where the single disjunct is a conjunction made of prop letter (if it occurs in the row with T) or negation of a prop letter (if it occurs in the row with F). – Mauro ALLEGRANZA Jan 11 '21 at 12:31
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@MauroALLEGRANZA I wrote the last value of the table wrong. It’s supposed to be F – hyperbolic76 Jan 11 '21 at 12:32
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See also this post – Mauro ALLEGRANZA Jan 11 '21 at 13:13
1 Answers
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My apologies if this should be a comment, I don't have the rep. It's been a while since I learned this, but isn't it going to be $P \oplus Q$ or $P \veebar Q$, the XOR/exclusive or operator? Unless there is more information that's not available, that fits all of your datapoints.
Dan Pollard
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1Your are right. It’s my mistake, I forgot to mention that I must only use ∨ ∧ ¬. I will edit the post. – hyperbolic76 Jan 11 '21 at 13:27
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Ah I see. In that case I agree with what you found - $(P\vee Q)\wedge (\neg P\vee \neg Q)$ works. – Dan Pollard Jan 11 '21 at 13:33