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Unformatted text preview: Show that A  B = ∅ → A ⊆ B. [Hints: (1) x ε A → x ∉ ∅ → ... . (2) A  B = ∅ → ∀ x( x ε A  B → x ε ∅ ). The contrapositive of the implication within the parentheses here is useful in dealing with the ellipsis in hint #1.] _________________________________________________________________ 9. (5 pts.) If f:X → Y is a function, f1 may be used to denote two quite different things. What are they? [Use complete sentences.] TEST1/MAD2104 Page 4 of 4 _________________________________________________________________ 10. (15 pts.) Suppose that f: → Ζ is the function defined by the formula f(x)= x , and suppose that A = {x ε  3 ≤ x ≤ 3} and B = {x ε  1 < x ≤ π }. Using appropriate notation, give each of the following. A  B = f(B) = f1 ({1,3}) = _________________________________________________________________ 11. (5 pts.) What is the value of the following sum of terms of a geometric progression? [Hint: You may wish to reindex the varmint.] 8 ∑ 2 j = j=1 _________________________________________________________________ 12. (5 pts.) Suppose g:A → B and f:B → C are functions. Prove exactly one of the following propositions. Indicate clearly which you are demonstrating. (a) If f g:A → C is injective, then g is injective. (b) If f g:A → C is surjective, then f is surjective....
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 Spring '08
 STAFF
 Logic, pts, Countable set

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