Transform $(phi vee psi) wedge (neg phi vee neg psi) $ to $ (phi wedge neg psi) vee (neg phi wedge psi)$...
$begingroup$
$(phi oplus psi) equiv (phi vee psi) wedge (neg phi vee neg psi) equiv (phi wedge neg psi) vee (neg phi wedge psi)$
I found the first one in a book and thought of the second one myself and was under the impression that I can transform one into the other using just the usual equivalences for classical propositional logic. How do I transform
$(phi vee psi) wedge (neg phi vee neg psi) $ to $ (phi wedge neg psi) vee (neg phi wedge psi)$ using just the usual equivalences?
propositional-calculus
asked Dec 4 '18 at 15:28
stevesteve
29427
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add a comment |
$begingroup$
$(phi oplus psi) equiv (phi vee psi) wedge (neg phi vee neg psi) equiv (phi wedge neg psi) vee (neg phi wedge psi)$
I found the first one in a book and thought of the second one myself and was under the impression that I can transform one into the other using just the usual equivalences for classical propositional logic. How do I transform
$(phi vee psi) wedge (neg phi vee neg psi) $ to $ (phi wedge neg psi) vee (neg phi wedge psi)$ using just the usual equivalences?
propositional-calculus
asked Dec 4 '18 at 15:28
stevesteve
29427
$endgroup$
add a comment |
$begingroup$
$(phi oplus psi) equiv (phi vee psi) wedge (neg phi vee neg psi) equiv (phi wedge neg psi) vee (neg phi wedge psi)$
I found the first one in a book and thought of the second one myself and was under the impression that I can transform one into the other using just the usual equivalences for classical propositional logic. How do I transform
$(phi vee psi) wedge (neg phi vee neg psi) $ to $ (phi wedge neg psi) vee (neg phi wedge psi)$ using just the usual equivalences?
propositional-calculus
asked Dec 4 '18 at 15:28
stevesteve
29427
$endgroup$
$(phi oplus psi) equiv (phi vee psi) wedge (neg phi vee neg psi) equiv (phi wedge neg psi) vee (neg phi wedge psi)$
I found the first one in a book and thought of the second one myself and was under the impression that I can transform one into the other using just the usual equivalences for classical propositional logic. How do I transform
$(phi vee psi) wedge (neg phi vee neg psi) $ to $ (phi wedge neg psi) vee (neg phi wedge psi)$ using just the usual equivalences?
propositional-calculus
propositional-calculus
asked Dec 4 '18 at 15:28
stevesteve
29427
asked Dec 4 '18 at 15:28
stevesteve
29427
asked Dec 4 '18 at 15:28
stevesteve
29427
asked Dec 4 '18 at 15:28
stevesteve
29427
asked Dec 4 '18 at 15:28
stevesteve
29427
29427
add a comment |
add a comment |
1 Answer
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I wrote down my question and instantly knew the answer. I just leave this here since I already typed it.
$(phi vee psi) wedge (neg phi vee neg psi) $
$equiv (phi wedge (neg phi vee neg psi)) vee (psi wedge (neg phi vee neg psi)) $
$equiv (phi wedge neg psi) vee (neg phi wedge psi)$
answered Dec 4 '18 at 15:28
stevesteve
29427
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
I wrote down my question and instantly knew the answer. I just leave this here since I already typed it.
$(phi vee psi) wedge (neg phi vee neg psi) $
$equiv (phi wedge (neg phi vee neg psi)) vee (psi wedge (neg phi vee neg psi)) $
$equiv (phi wedge neg psi) vee (neg phi wedge psi)$
answered Dec 4 '18 at 15:28
stevesteve
29427
$endgroup$
add a comment |
$begingroup$
I wrote down my question and instantly knew the answer. I just leave this here since I already typed it.
$(phi vee psi) wedge (neg phi vee neg psi) $
$equiv (phi wedge (neg phi vee neg psi)) vee (psi wedge (neg phi vee neg psi)) $
$equiv (phi wedge neg psi) vee (neg phi wedge psi)$
answered Dec 4 '18 at 15:28
stevesteve
29427
$endgroup$
add a comment |
$begingroup$
I wrote down my question and instantly knew the answer. I just leave this here since I already typed it.
$(phi vee psi) wedge (neg phi vee neg psi) $
$equiv (phi wedge (neg phi vee neg psi)) vee (psi wedge (neg phi vee neg psi)) $
$equiv (phi wedge neg psi) vee (neg phi wedge psi)$
answered Dec 4 '18 at 15:28
stevesteve
29427
$endgroup$
I wrote down my question and instantly knew the answer. I just leave this here since I already typed it.
$(phi vee psi) wedge (neg phi vee neg psi) $
$equiv (phi wedge (neg phi vee neg psi)) vee (psi wedge (neg phi vee neg psi)) $
$equiv (phi wedge neg psi) vee (neg phi wedge psi)$
answered Dec 4 '18 at 15:28
stevesteve
29427
answered Dec 4 '18 at 15:28
stevesteve
29427
answered Dec 4 '18 at 15:28
stevesteve
29427
answered Dec 4 '18 at 15:28
stevesteve
29427
29427
add a comment |
add a comment |
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