1. Why is it important to recognize the converse and the con- trapositive of a conditional statement?
1. Why is it important to recognize the converse and the con- trapositive of a conditional statement?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 27E
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Transcribed Image Text:1. Why is it important to recognize the converse and the con-
trapositive of a conditional statement?
2. How does the strong form of induction differ from basic
mathematical induction?
3. What mathematical structure previously studied has the
same properties as (logical statements, V, ^,~)?
Transcribed Image Text:6. Let A = {x |x is a real number and 0 <x < 1},
B = {x |x is a real number and x? +1= 0},
C = {x | x = 4m, m e Z}, D = {0, 2, 4, 6 ...}, and
E = (x |x € Z and x² < 100}.
(a) Identify the following as true or false.
%3D
(i) CCD
(iii) (4, 16} C E
(ii) {4, 16} CC
(iv) DCD
(v) BCØ
(b) Identify the following as true or false.
(i) CNE¢ (CUE)
(ii) øC (ANB)
(iv) CUECD
(iii) CND= D
(v) ANDCANC
7. Let A = {x | x = 2n, n € Z*).
B = {x |x = 2n + 1, n € Z*), C = {x |x = 4n, n €
Z*), and D = {x | x(r² – 6x +8) = 0, x e Z}. Use Z as
the universal set and find
(a) AUB
(b) Ā
(c) (AN D) ® (AN B) (d) AUC
(е) А- С
8. Draw a Venn diagram to represent (a) ANB and
(b) ĀnB.
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