5. (Exploration 1) Examine each of the following formulas about sets and set operations. Show by means of a Venn diagram whether or not the formula is correct for all sets. If the formula is not correct, give a specific counterexample. (You can think of each formula as the con- clusion to a conditional sentence that begins "If A, B, and C are sets, then...". Thus a counterexample consists of specific sets that, when substituted, give a false statement.) Also, if the formula is not correct, find, if possible, an alternative expression to put on the right-hand side of the equation, to produce a correct formula. a) (A U B) nC=AU (BNC). b) (An B)' = A' B'. c) A (BUC) = (A - B) U (A - C). d) (AB) C = (A - C) (B − C).
5. (Exploration 1) Examine each of the following formulas about sets and set operations. Show by means of a Venn diagram whether or not the formula is correct for all sets. If the formula is not correct, give a specific counterexample. (You can think of each formula as the con- clusion to a conditional sentence that begins "If A, B, and C are sets, then...". Thus a counterexample consists of specific sets that, when substituted, give a false statement.) Also, if the formula is not correct, find, if possible, an alternative expression to put on the right-hand side of the equation, to produce a correct formula. a) (A U B) nC=AU (BNC). b) (An B)' = A' B'. c) A (BUC) = (A - B) U (A - C). d) (AB) C = (A - C) (B − C).
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:5. (Exploration 1) Examine each of the following formulas about sets and set operations. Show
by means of a Venn diagram whether or not the formula is correct for all sets. If the formula
is not correct, give a specific counterexample. (You can think of each formula as the con-
clusion to a conditional sentence that begins "If A, B, and C are sets, then...". Thus a
counterexample consists of specific sets that, when substituted, give a false statement.)
Also, if the formula is not correct, find, if possible, an alternative expression to put on the
right-hand side of the equation, to produce a correct formula.
a) (AUB) nC = AU (BNC).
B'.
b) (ANB)' = A'
c) A (BUC) =
(A - B) U (A - C).
d) (AB) C = (AC) - (B − C).
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