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# lasthw - f is surjective onto B and g ◦ f is injective...

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Math 8 Homework 1 Write an English sentence that is the negation of “You can run, but you can’t hide.” 2 Take N to be the universal set. Write the set { 1 , 100 , 101 , 102 , 103 , . . . } in the form { x | P ( x ) } . 3 Prove that if A B then A × A B × B . 4 Let I = { 1901 , 1902 , 1903 , . . . , 2000 } . For all i I , let A i be the set of all people born in the year i . (a) Are you an element of i I A i ? (b) Are you an element of ( i I A i ) ( 1901 i 1910 A i )? 5 Let X = {- 1 , 0 , 1 } . Let be the equivalence relation on X given by x y x 2 = y 2 . What is the corresponding partition of X ? 6 Suppose f : A B and g : B C are functions. Prove that if
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Unformatted text preview: f is surjective onto B and g ◦ f is injective then g is injective. 8 Prove by induction that n ! > 2 n for all n ≥ 4. 9 Prove that if A ≈ B then A × A ≈ B × B . 10 Label the following sets ﬁnite, countably inﬁnite, or uncountably inﬁnite. You don’t have to prove anything. (a) ∅ (b) Z (c) Z × Z (d) The set of all functions from Z to R (e) The set of all stars in the galaxy. 1...
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