Let A = {t, u, v, w, and let S₁ be the set of all subsets of A that do not contain w, and S₂ the set of all subsets of A that contain w. (a) Find S₁. (Enter your answer in set-roster notation. Enter EMPTY or for the empty set.) (b) Find S₂. (Enter your answer in set-roster notation. Enter EMPTY or Øø for the empty set.)
Let A = {t, u, v, w, and let S₁ be the set of all subsets of A that do not contain w, and S₂ the set of all subsets of A that contain w. (a) Find S₁. (Enter your answer in set-roster notation. Enter EMPTY or for the empty set.) (b) Find S₂. (Enter your answer in set-roster notation. Enter EMPTY or Øø for the empty set.)
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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Transcribed Image Text:Let A = {t, u, v, w}, and let S₁ be the set of all subsets of A that do not contain w, and S₂ the set of all subsets of A that contain w.
(a) Find S₁. (Enter your answer in set-roster notation. Enter EMPTY or for the empty set.)
(b) Find S₂. (Enter your answer in set-roster notation. Enter EMPTY or for the empty set.)
(c) Are S₁ and S₂ disjoint?
Yes
No
(d) Compare the sizes of S₁ and S₂.
S₁ has
(e) How many elements are in S₁ US₂?
elements, and S₂ has
(f) What is the relation between S₁ U S₂ and P(A)?
OS₁ U S₂ is equal to P(A)
S₁ US₂ is not a subset of P(A)
OP(A) is a proper subset of S₁ U S₂
OP(A) is not a subset of S₁ U S₂
S₁ U S₂ is a proper subset of P(A)
elements. Therefore, the size of S₁
---Select---
the size of S₂.
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