answer 1 only. Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfyrequired properties.1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B.b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) C (A x B) u(C x D).2. a. Prove using the formal definition of a limit that the following sequence converges:+oo-n3 + 2n- 21213 + и + 41=1b. Let {a,} be a sequence of real numbers. We say that {a;} decreases without bound,written lim an = -00, iff11=1(VM < 0)(3N > 0) (n € N)(n > N = an < M).Show that lim (-n*) = -0o.

Answered: Image /qna-images/answer/181f8d50-fafc-41df-9d45-f3314b194cd5.jpg

Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy required properties. 1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B. b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) (A x B) U (C x D).

Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy required properties. 1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B. b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) (A x B) U (C x D).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

answer 1 only.

Proofs must be clear, coherent, concise, and complete, and examples should be verified to satisfy
required properties.
1. a. Show that for all sets A, B, and C, if A CBUC, then A nc+ø or A C B.
b. Disprove: For all sets A, B, C, and D, (AUC) x (BUD) C (A x B) u(C x D).
2. a. Prove using the formal definition of a limit that the following sequence converges:
+oo
-n3 + 2n
- 21
213 + и + 4
1=1
b. Let {a,} be a sequence of real numbers. We say that {a;} decreases without bound,
written lim an = -00, iff
11=1
(VM < 0)(3N > 0) (n € N)(n > N = an < M).
Show that lim (-n*) = -0o.

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