Exercise 1.2.3. Decide which of the following represent true statements about the nature of sets. For any that are false, provide a specific example where the statement in question does not hold. (a) If A₁ 2 A2 2 A3 2 A4... are all sets containing an infinite number of elements, then the intersection 1 An is infinite as well. (b) If A₁ 2 A2 2 A3 2 A4 are all finite, nonempty sets of real numbers, then the intersection 1 An is finite and nonempty. (c) An (BUC) = (ANB) UC. (d) An (BNC) = (ANB)nc. (e) An (BUC) = (ANB) u (ANC).
Exercise 1.2.3. Decide which of the following represent true statements about the nature of sets. For any that are false, provide a specific example where the statement in question does not hold. (a) If A₁ 2 A2 2 A3 2 A4... are all sets containing an infinite number of elements, then the intersection 1 An is infinite as well. (b) If A₁ 2 A2 2 A3 2 A4 are all finite, nonempty sets of real numbers, then the intersection 1 An is finite and nonempty. (c) An (BUC) = (ANB) UC. (d) An (BNC) = (ANB)nc. (e) An (BUC) = (ANB) u (ANC).
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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Please solve for the (d) and (e)
Please solve for the (d) and (e)
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Transcribed Image Text:Exercise 1.2.3. Decide which of the following represent true statements about
the nature of sets. For any that are false, provide a specific example where the
statement in question does not hold.
(a) If A1 2 A2 2 A3 2 A4 are all sets containing an infinite number of
elements, then the intersection - An is infinite as well.
(b) If A₁ 2 A22 A3 2 A4 are all finite, nonempty sets of real numbers,
then the intersection 1 An is finite and nonempty.
(c) An (BUC) = (ANB)UC.
(d) An (BnC) = (ANB)nc.
(e) An (BUC) = (ANB)u (ANC).
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