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Material Type: Exam; Professor: Toida; Class: DISCRETE STRUCTURES; Subject: Computer Science; University: Old Dominion University; Term: Unknown 1989;
Typology: Exams
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CS 381 Test
July, 2006
(b) ∀x∃y¬L(x, y) For every number there is a number that is not less than that. i.e. Every number is not greater than some number.
(c) ∀x∃y[[I(x) ∧ I(y)] → L(x, y)]] For every number x there is a number y such that if x and y are integer, then x is gretaer than y. i.e. For every integer, there is an integer that is less than that. i.e. Every integer is greater than some integer.
(d) ∀x∃I(y)L(I(x), y) This is not a proposition (well-formed formula) because an atomic formula I(x) is an argument of another atomic formula L(x, y).
(b) Some number is greater than or equal to every number. Every number is less than some number.
(c) Some numbers are even only if they are integer. Every number is even and not integer.
¬∀xI(x)
(b) A (every) number is even only if it is integer.
∀x[E(x) → I(x)]
(c) It is not necessary for a number to be integer that it is even.
¬∀x[I(x) → E(x)], which I prefer, or ∀x¬[I(x) → E(x)]