Exam s 2-4 - a and b are even or a and b are odd 4(10 pts...

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MATH 290 – 27 MAY 2010 – EXAM 2 Answer all of the following questions on the answer sheets provided. Show all work, as partial credit may be given. This exam will be counted out of a total of 60 points. 1. (10 pts.) Prove that for any integers a , b , and c , if a | b and a | c then a | ( b - c ). 2. (10 pts.) Prove by contrapositive that for all natural numbers n , if n 2 is odd then n is odd. 3. (14 pts.) Prove that for all integers a and b , a + b is even if and only if
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Unformatted text preview: a and b are even or a and b are odd. 4. (10 pts.) Prove that for all sets A and B , if A ⊆ B then P ( A ) ⊆ P ( B ). 5. (10 pts.) Prove that for all sets A , B , and C , ( A ∪ B ) ∩ C ⊆ A ∪ ( B ∩ C ). 6. (10 pts.) Let A = { A α : α ∈ Δ } be an indexed family of sets. Prove that if there exists a set B such that for all α ∈ Δ, A α ⊆ B , then [ α ∈ Δ A α ⊆ B ....
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