Predicate Logic Flashcards
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