1. Given a set X and a subset A CX, define a function ƒÃ : X → {0, 1} by setting f₁(x) 1 if ¤ ¤ A and ƒÂ(x) = 0 if x ‡ A. If B is also a subset of X, define (ƒ^ƒB)(x) = ƒ^(x)ƒÂ(x). = (a) Work out ƒAƒв when X = {1, 2, 3, 4, 5}, A = {2, 4, 5} and B = {1,2,5}. (b) What subset, if any, does ƒÃƒÂ correspond to? (c) Define f' by f'(x) = 1 − ƒ₁(x). What subset, if any, does f' correspond to? (d) Form combinations of fA and fB which represent (i) the union of A and B; (ii) the symmetric difference A + B = (A \ B) U (B \ A) of A and B.
1. Given a set X and a subset A CX, define a function ƒÃ : X → {0, 1} by setting f₁(x) 1 if ¤ ¤ A and ƒÂ(x) = 0 if x ‡ A. If B is also a subset of X, define (ƒ^ƒB)(x) = ƒ^(x)ƒÂ(x). = (a) Work out ƒAƒв when X = {1, 2, 3, 4, 5}, A = {2, 4, 5} and B = {1,2,5}. (b) What subset, if any, does ƒÃƒÂ correspond to? (c) Define f' by f'(x) = 1 − ƒ₁(x). What subset, if any, does f' correspond to? (d) Form combinations of fA and fB which represent (i) the union of A and B; (ii) the symmetric difference A + B = (A \ B) U (B \ A) of A and B.
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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1. Given a set X and a subset AC X, define a function ƒÃ : X → {0, 1} by setting
f₁(x) = 1 if x € A and ƒ₁(x) = 0 if x ‡ A. If B is also a subset of X, define
(ƒAƒB)(x) = ƒ^(x)ƒÂ(x).
(a) Work out fAfB when X = {1,
(b) What subset, if any, does ƒAƒB correspond to?
(c) Define f' by f(x) = 1 - f₁(x). What subset, if any, does f' correspond
to?
2, 3, 4, 5},
., 2, 3, 4, 5}, A = {2, 4, 5} and B
{2, 4, 5} and B = {1,2,5}.
(d) Form combinations of fд and fв which represent
(i) the union of A and B;
(ii) the symmetric difference A + B
=
(A \ B) U (B\ A) of A and B.
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