30. (i) Verify that Hall's marriage condition is satisfied for the family {A₁, A₂, A3, A4, A5, A6} where A₁ = {a, c}, A₂ = {b, c), A, = {a, c, d, e}, A4 = {b, d, e, f}, As = {a, e} and A6 = {a, b}. (ii) Verify that Hall's marriage condition is not satisfied for the family {4₁, A2, A3, A4, A5, A6) where A₁ = {a, b, c), A₂ = {b, c), A3 = {c, e, f}, (a b)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 16E
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Topic: discrete mathematics
30.
(i) Verify that Hall's marriage condition is satisfied for the family {A,, A2,
A3, A4, As, A6} where A, = {a, c}, A2 = {b, c}, A, = {a, c, d, e}, A =
{b, d, e, f}, As = {a, e} and A, = {a, b}.
(ii) Verify that Hall's marriage condition is not satisfied for the family {A,
A2, A3, A4, As, A6} where A, = {a, b, c}, A2 {b, c}, A, {c, e, f},
A = {a, b}, A, = {a, c} and A, = {d, e, f}.
%3D
Transcribed Image Text:30. (i) Verify that Hall's marriage condition is satisfied for the family {A,, A2, A3, A4, As, A6} where A, = {a, c}, A2 = {b, c}, A, = {a, c, d, e}, A = {b, d, e, f}, As = {a, e} and A, = {a, b}. (ii) Verify that Hall's marriage condition is not satisfied for the family {A, A2, A3, A4, As, A6} where A, = {a, b, c}, A2 {b, c}, A, {c, e, f}, A = {a, b}, A, = {a, c} and A, = {d, e, f}. %3D
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