Predicate Logic Flashcards
(23 cards)
Universal Quantifier
Used to assert that all entities have some property or properties
(x), (y), or (z)
Universal quantifier
All things move
(x)(Mx)
Universal Quantifier corresponds with…
⊃ (conditional hook)
Existential Quantifier
Assert some individual or individuals, at least one, have one or more properties
(∃x)
Existential Quantifier
Some things move
(∃x)(Mx)
Existential Quantifier corresponds with…
. (conjunction)
All A’s are B’s
(x)(Ax ⊃ Bx)
~(∃x)(Ax * ~Bx)
(x)(Ax ⊃ Bx)
~(∃x)(Ax * ~Bx)
All A’s are B’s
No A’s are B’s
(x)(Ax ⊃ ~Bx)
~(∃x)(Ax . Bx)
(x)(Ax ⊃ ~Bx)
~(∃x)(Ax . Bx)
No A’s are B’s
Some A’s are B’s
(∃x)(Ax . Bx)
~(x)(Ax ⊃ ~Bx)
(∃x)(Ax . Bx)
~(x)(Ax ⊃ ~Bx)
Some A’s are B’s
Some A’s are not B’s
(∃x)(Ax . ~Bx)
~(x)(Ax ⊃ Bx)
(∃x)(Ax . ~Bx)
~(x)(Ax ⊃ Bx)
Some A’s are not B’s
Some dogs and cats are rabid
(∃x)(Dx . Rx) . (∃x)(Cx . Rx)
(∃x)(Dx . Rx) . (∃x)(Cx . Rx)
Some dogs and cats are rabid
Women and children are exempt from the draft
(x)[(Wx v Cx) ⊃ Ex]
(x)[(Wx v Cx) ⊃ Ex]
Women and children are exempt from the draft
Only those who study will pass the test
(x)(Px ⊃ Sx)
(x)(Px ⊃ Sx)
Only those who study will pass the test
Only, none but, none except
BE CARFEUL WITH THE ORDER OF THESE WORDS AND WHAT THE LOGIC OF THE SENTENCE INFERS
