lo. If A = $1,2,3,43 B= $3,4,5,63 ten Draws the
rodeo venn
diagram of
ii) ADB i) A-B iN) B-A
i AUB
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Answer:
First, we find A∪(B∩C)
Consider B∩C= {1, 2, 3, 4, 5 ,6} ∩ {2, 4, 6, 7} = {4,6}
A∪(B∩C) = {0,1,2,3,4} U = {4, 6} , = { 0, 1, 2, 3, 4, 6}. (1)
Next, consider A∪B = {0,1, 2, 3, 4} ∪ {1, -2, 3, 4, 5, 6}
= { -2, 0, 1, 2, 3, 4, 5, 6},
A∪C, = {0, 1, 2, 3, 4} ∪ {2, 4, 6, 7} = {0, 1, 2, 3, 4, 6, 7}.
Thus, (A∪B)∩(A∪C) = {-2, 0, 1, 2, 3, 4, 5, 6} ∩ {0, 1, 2, 3, 4, 6, 7}
= {0, 1, 2, 3, 4, 6}. (2)
From (1) and (2), we get A∪(B∩C)=(A∪B)∩(A∪C)
(ii) Using Venn diagram, we have
From (2) and (5) it is verified that A∪(B∩C)=(A∪B)∩(A∪C).
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