10. (a) Show that relativecomplementation is not commuta-tive; that is, the equality A \ B = B \ A can fail.(b) Show that relative complementation is not associa-tive: (A \ B) \ C = A \ (B \ C) can fail.11. Let A = {a,b,c} and B = {a, b, d}.(a) List or draw the ordered pairs in A × A.(b) List or draw the ordered pairs in A x B.(c) List or draw the set {(x, y) = A x B: x = y}.12. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4}.(a) How many ordered pairs are in S × T? T × S?(b) List or draw the elements in the set{(m, n) e S x T:m

Answered: 10. (a) Show that relative…

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

10. (a) Show that relative
complementation is not commuta-
tive; that is, the equality A \ B = B \ A can fail.
(b) Show that relative complementation is not associa-
tive: (A \ B) \ C = A \ (B \ C) can fail.
11. Let A = {a,b,c} and B = {a, b, d}.
(a) List or draw the ordered pairs in A × A.
(b) List or draw the ordered pairs in A x B.
(c) List or draw the set {(x, y) = A x B: x = y}.
12. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4}.
(a) How many ordered pairs are in S × T? T × S?
(b) List or draw the elements in the set
{(m, n) e S x T:m<n}.

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Part (10):- (a):-

Show that relative complementation is not commutative; that is, the equality $A \ B = B \ A$ can fail.