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10 questions
p→q, p implies q also written (p→q)∧p⟹q
Modus Ponnens
Modus Tollens
Disjunctive Syllogism
Hypothetical Syllogism
(p→q), ∼q implies ∼p
Modus Ponens
Modus Tollens
Disjunctive Syllogism
Simplification
(p→q), (q→r) implies (p→r)
Modus Ponens
Modus Tollens
Distributive Syllogism
Hypothetical Syllogism
(p∨q), ∼p implies q
Modus Ponens
Disjunctive Syllogism
Simplification
Addition
"If A works hard, then either B or C will enjoy themselves". " If B enjoys himself then A will not work hard".
"If D enjoys himself, then C will not".
Therefore, " if A works hard, D will not enjoy himself". Formulate these sentences
A→(B∧C), B⟶A, D⟶C Therefore A →D
A→(B∨C), B⟶∼A, D⟶∼C Therefore A→∼D
None of the above
p∨q⟺q∨p and p∧q⟺q∧p
Commutative laws
De Morgan’s laws
Idempotent laws
Absorption law
p∨p⟺p and p∧p⟺p
De Morgan’s laws
modus ponens
Associative laws
Idempotent laws
which one of the following is an absorption law?
p∧(p∨q)⟺p and p∨(p∧q)⟺p
p∧p⟺p and p∨p⟺p
p∧q⟺q∧p and p∨q⟺q∨p
p∨(q∨r)⟺(p∨q)∨r and p∧(q∧r)⟺(p∧q)∧r
∼(p∨q)⟺∼p∧∼q and ∼(p∧q)⟺∼p∨∼q
Distributive laws
Associative laws
De Morgan’s laws
Absorption law
p∧(q∨r)⟺(p∧q)∨(p∧r) and p∨(q∧r)⟺(p∨q)∧(p∨r)
Associative laws
Distributive laws
Absorption law
none of the above
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