Set A,B and C are: A = {1, 2, 4, 8, 10 12,14}, B = { 1,2, 3 ,4, 5 }
and C { 2, 5,7,9,11, 13}.
Find A BC , A B C, A BC and (B~C)
Mecrin:
A intersection b union c, A union B union C,A union B intersection C and (B~C)
Answers
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A = { 1, 2, 4, 8, 10, 12, 14)
B = (1,2 , 3, 4, 5, }
C = { 2, 5, 7, 9, 11, 13 }
A ∧ B U C is probably either (A ∧ B) U C or A ∧ (B U C). Check question...
(A ∧ B) U C = {1, 2, 4} U C = {1, 2, 4, 5, 7, 9, 11, 13} --- (1)
A ∧ (B U C) = A ∧ {1, 2, 3, 4, 5, 7, 9, 11, 13} = {1, 2, 4} --- (2)
(1) is always a subset of (2)...
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A U B U C = (A U B) U C = A U (B U C) both are same
= { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14 }
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A U B∧ C
(A U B) ∧ C = {1, 2, 3, 4, 5, 8, 10, 12, 14 } ∧ C = { 2, 5 }
A U (B ∧ C) = A U {2, 5 } = {1, 2, 4, 5, 8, 10, 12, 14 }
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B - C = B - (B ∧ C) = { 1, 3, 4 }
B = (1,2 , 3, 4, 5, }
C = { 2, 5, 7, 9, 11, 13 }
A ∧ B U C is probably either (A ∧ B) U C or A ∧ (B U C). Check question...
(A ∧ B) U C = {1, 2, 4} U C = {1, 2, 4, 5, 7, 9, 11, 13} --- (1)
A ∧ (B U C) = A ∧ {1, 2, 3, 4, 5, 7, 9, 11, 13} = {1, 2, 4} --- (2)
(1) is always a subset of (2)...
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A U B U C = (A U B) U C = A U (B U C) both are same
= { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14 }
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A U B∧ C
(A U B) ∧ C = {1, 2, 3, 4, 5, 8, 10, 12, 14 } ∧ C = { 2, 5 }
A U (B ∧ C) = A U {2, 5 } = {1, 2, 4, 5, 8, 10, 12, 14 }
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B - C = B - (B ∧ C) = { 1, 3, 4 }
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