Laws of logic
Law of Detachment:
Law of Detachment:
Premise: If I play baseball, then I need a glove. p
®
q
Premise: I play baseball p
Conclusion:
\
Law of Contrapositive: p
®
q
\
Law of Modus Tollens: p
®
q
~ q
\
Chain Rule:
Premise: If today is Monday, then I go to school. p
®
q
Premise: If I go to school, then I have homework. q
®
r
Conclusion:
\
Law of Disjunctive Inference:
Premise: Mrs. Ryan has coffee or tea at every meal. p v q
Premise: Mrs. Ryan does not have coffee at dinner. ~ q
Conclusion:
\
Law of Double Negation: ~ (~p) =
DeMorgan’s Laws: ~ (p v q) =
~ (p
Ù
q) =
Law of Simplification: p
Ù
q or p
Ù
q
\
p
\
q
Law of Conjunction: p
q
\
p
Ù
q
Law of Disjunctive Addition:
p
\
p v q
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