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Unformatted text preview: your answer. 3. (16 pts.) Let A be a set and consider the partial order ⊆ on P ( A ). For some natural number n , let B = { B 1 , B 2 , ..., B n } be a family of subsets of A . Prove that the least upper bound (that is, the supremum) of B with respect to the partial order ⊆ is S = n [ k =1 B k . 4. Consider the function f ( x ) = x1 x + 3 . (a) (4 pts.) Find the implied domain of f . (b) (4 pts.) Find the range of f . (c) (8 pts.) Deﬁne the function g to be the restriction of f to the interval (3 , ∞ ), that is, g = f  (3 , ∞ ) . Find Rng ( g ), the range of g . Justify your answer with a proof, that is, prove that for every y ∈ Rng ( g ) there is an x ∈ (3 , ∞ ) such that f ( x ) = y ....
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This note was uploaded on 03/05/2011 for the course MATH 290 taught by Professor Alligood,k during the Fall '08 term at George Mason.
 Fall '08
 Alligood,K
 Math, Advanced Math

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