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# All lions are erce 2 some lions do not drink coee 3

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Unformatted text preview: is a snurd.” Solution: ¬∃x S(x) What is this equivalent to? Solution: ∀x ¬ S(x) Transla\$on (cont) ༉  U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “All ﬂeegles are snurds.” Solution: ∀x (F(x)→ S(x)) Transla\$on (cont) ༉  U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “Some ﬂeegles are thingamabobs.” Solution: ∃x (F(x) ∧ T(x)) Transla\$on (cont) ༉  U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “No snurd is a thingamabob.” ¬ “Some snurd is a thingamabob.” Solution: ¬∃x (S(x) ∧ T(x)) Solution: ∀x (¬S(x) ∨ ¬T(x)) Transla\$on (cont) ༉  U = {ﬂeegles, snurds, thingamabobs} F(x): x is a ﬂeegle S(x): x is a snurd T(x): x is a thingamabob “If any ﬂeegle is a snurd then it is also a thingamabob.” Solution: ∀x ((F(x) ∧ S(x)) → T(x)) System Speciﬁca\$on Example ༉  For example, translate into predicate logic: ༉  “Every mail message larger than one megabyte will be compressed.” ༉  “If a user is active, then at least one network link will be available.” ༉  Decide on predicates and domains for the variables: ༉  Let L(m, y) be “Mail message m is larger than 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.” ༉  No...
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