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# Calculusinlogicoponal

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Unformatted text preview: y megabytes.”    Let C(m) denote “Mail message m will be compressed.”    Let A(u) represent “User u is active.”    Let S(n, x) represent “Network link n is state x.    Now we have:  Lewis Carroll Example  Charles Lutwidge Dodgson     (AKA Lewis Caroll)          (1832‐1898)    The ﬁrst two are called premises and the third is called the  conclusion.   1.  2.  3.    “All lions are ﬁerce.”  “Some lions do not drink coﬀee.”  “Some ﬁerce creatures do not drink coﬀee.”   Here is one way to translate these statements to predicate  logic. Let P(x), Q(x), and R(x) be the propositional functions  “x is a lion,” “x is ﬁerce,” and “x drinks coﬀee,” respectively.  ∀x (P(x)→ Q(x)) 2.  ∃x (P(x) ∧ ¬R(x)) 3.  ∃x (Q(x) ∧ ¬R(x)) 1.    Later we will see how to prove that the conclusion follows  from the premises.  Some Predicate Calculus  Deﬁni*ons (op#onal)    An assertion involving predicates and quantiﬁers is valid if  it is true       for all domains   every propositional function  substituted for the predicates in the  assertion.  Example:      An assertion involving predicates is satisﬁable if it is true       for some domains   some propositional functions that can be substituted for  the  predicates in the assertion.       Otherwise it is unsatisﬁable.      Example:                                     not valid but satisﬁable       Example: ...
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## This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

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