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23 Cards in this Set
- Front
- Back
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Idempotence
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p ∨ p ≡ p
p ∧ p ≡ p |
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excluded middle
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p ∨ ¬ p ≡ T
p ∧ ¬ p ≡ F |
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identity
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p ∨ F ≡ p
p ∧ T ≡ p |
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strictnes
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p ∨ T ≡ T
p ∧ F ≡ F |
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associativity
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(p ∨ q) ∨ r ≡ (p ∨ q) ∨ r
(p ∧ q) ∨ r ≡ (p ∧ q) ∨ r |
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commutativity
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p ∨ q ≡ q ∨ p
p ∧ q ≡ q ∧ p |
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ditributivity
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p ∨ ( q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
p ∧ ( q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) |
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de Morgan
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¬(p∨q)≡(¬p)∧(¬q)
¬(p∧q)≡(¬p)∨(¬q) |
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p xor q
in ands, nots and ors |
p xor q ≡ (p∨q)∧(¬p∧q)
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negated and, and equivelant in "basic" connectives
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p↑q ≡ ¬(p ∧ q)
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negated or, and equivelant in "basic" connectives
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p↓q ≡ ¬(p ∨ q)
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¬p in negated form
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¬p ≡ p↑p
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p ∨ q in nots and negated
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p∨q ≡ ¬p↑¬q
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p ⇒ q
in nots and negated |
¬p ∨ q
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state in terms of implication:
normal, converse, inverse contrapositive |
p ⇒ q
q ⇒ r ¬p ⇒ ¬q ¬q ⇒ ¬r |
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which is true:
original = contrapoistive original = covnerse converse = contrapositive converse = inverse |
T
F F T |
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iff, in implys
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p ⇒ q ∧ q ⇒ r
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∃x,p(x) ≡ de morgan
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¬(∃x,p(x)) ≡ ∀x, ¬ p(x)
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∀x,p(x) ≡ demorgan
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¬(∀x,p(x)) ≡ ∃x, ¬ p(x)
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values of A and E, where they are restricted by a type r(x).. write this logically
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∀x,r(x) ⇒ p(x)
∃x, r(x) ∧ p(x) |
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∀x,r(x) ⇒ p(x)
apply de morgans law |
¬(∃x, r(x) ∧ p(x)) ≡ ∀x,r(x) ⇒ ¬p(x)
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∃x, r(x) ∧ p(x)
apply de morgans law |
¬(∀x,r(x) ⇒ p(x)) ≡ ∃x, r(x) ∧ ¬p(x)
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∃y,∃x ≡ ∃x,∃y
∀y,∀x, ≡ ∀x,∀y, ∀y,∃x ≡ ∀x,∃y Which is true |
T
T F |
