Explicație pas cu pas:
[tex]x \leqslant 8[/tex]
A = {0, 1, 2, 3, 4, 5, 6, 7, 8}
[tex]x : 3 \: si \: x \leqslant 24[/tex]
B = {0, 3, 6, 9, 12, 15, 18, 21, 24}
[tex](x - 1) : 4 \: si \: x < 27[/tex]
[tex]x - 1 = 0 \implies x = 1 \\x - 1 = 4 \implies x = 5 \\ x - 1 = 8 \implies x = 9 \\ x - 1 = 12 \implies x = 13 \\ x - 1 = 16 \implies x = 17 \\ x - 1 = 20 \implies x = 21 \\ x - 1 = 24 \implies x = 25 \\ x - 1 = 28 \implies x = 29[/tex]
C = {1, 5, 9, 13, 17, 21, 25}
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A∪B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 18, 21, 24}
A∩B = {0, 3, 6}
A∪C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 17, 21, 25}
A∩C = {1, 5}
B∪C = {0, 1, 3, 5, 6, 9, 12, 13, 15, 17, 18, 21, 24, 25}
B∩C = {9, 21}
A∪B∪C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 15, 17, 18, 21, 24, 25}
A∩B∩C = Ø
A∪(B∩C) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21}
(A∪B)∩C = {1, 5, 9, 21}
(A∩B)∪(B∩C) = {0, 3, 6, 9, 21}
A∪B∩Ø = Ø
