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2009-11-10T20:54:00+01:00
Jeśli x∈ R
A={x : x ≥ 12 } = <12, +∞)
B= {x : 0 < x ≤ 13 } = (0, 13>
C= { x : 9 ≤ x ≤ 20 } = <9, 20>

A'=(-∞, 12)
B'=(-∞, 0> U (13, +∞)
C'=(-∞, 9) U (20, +∞)
A' U B' = (-∞, 12) U [(-∞, 0> U (13, +∞)] = (-∞, 12) U (13, +∞)
A' п B' = (-∞, 12) п [(-∞, 0> U (13, +∞)] = (-∞, 0>
(A п B)' п C =( (<12, +∞) п [(0, 13>] )' п <9, 20> = ( <12, 13> )' п <9, 20> = [(-∞, 12 ) U (13, +∞)] п <9, 20> = <9, 12) U (13, 20>
(A υ C)' υ B = ( <12, +∞) U <9, 20> )' U (0, 13> = ( <9, +∞) ) ' U (0, 13> = (-∞, 9) U (0, 13> = (-∞, 13>

U jest zbiorem wszystkich liczb naturalnych od 0 do 20.
Jeśli x∈ U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
A={x : x ≥ 12 } = {12, 13, 14, 15, 16, 17, 18, 19, 20}
B= {x : 0 < x ≤ 13 } = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
C= { x : 9 ≤ x ≤ 20 } = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A'={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
B'={0, 14, 15, 16, 17, 18, 19, 20}
C'={0, 1, 2, 3, 4, 5, 6, 7, 8}
A' U B' = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18,19, 20} = (zbiór) U \ {12, 13}
A' п B' = {0}
(A п B)' п C = ( {12, 13} ) ' п {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 19, 20} п {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} = {9, 10, 11, 14, 15, 16, 17, 18, 19, 20}
(A υ C)' υ B = ( {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} ) ' U {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} = {0, 14, 15, 16, 17, 18, 19, 20} U {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} = (zbiór) U
2009-11-10T20:59:41+01:00
A' υ B' = (0;11) U {0} U (13;20) = <0;11) U (13;20)
A' п B' = (0;11) п {0} п (13;20) = θ
(A п B)' п C = <12;13> п <9,20> = <9;13>
(A υ C)' υ B = <9;20> U (0;13> = (0;20>