03Fe3 - by Smith, Eggen, and St. Andre: 5 th ed.): Chapter...

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Unformatted text preview: by Smith, Eggen, and St. Andre: 5 th ed.): Chapter 2 . Numbers: • real numbers = R • natural numbers = N = { 1 , 2 , 3 , 4 , . . . } • integers = Z = { , ± 1 , ± 2 , ± 3 , ± 4 , . . . } • rational numbers = Q = n p q ∈ R : p, q ∈ Z and q 6 = 0 o 1. Let A and B be sets. 1a. By deﬁnition, the power set of A is: P ( A ) = { C : } . 1b. Show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) . 2. Let A = { A i : i ∈ N } be an indexed family of sets. Let k, m ∈ N with k ≤ m . Show that k [ i =1 A i ⊆ m [ i =1 A i . 3. 3a. By deﬁnition, a is even if and only if . 3b. Let a = 2, a 1 = 4, a 2 = 6, and a n +2 = 5 a n-1 for each n ∈ N . Show that a n is even for each n ∈ { , 1 , 2 , 3 , 4 , . . . } . 4. 4a. By deﬁnition, a is odd if and only if . 4b. Let a 1 = 1, a 2 = 3, and a n +2 = 2 a n +1 + a n for each n ∈ N . Show that a n is odd for each n ∈ N ....
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This note was uploaded on 12/13/2011 for the course MATH 300 taught by Professor Staff during the Fall '11 term at South Carolina.

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03Fe3 - by Smith, Eggen, and St. Andre: 5 th ed.): Chapter...

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