Consider A = {1,2,3,4,5,6,7,8,9} and let B1 = {5,6,7} , B2 = {2,4,5,9} and B3 = {3,4,5,6,8,9}. Find the minsets generated by B1, B2, and B3. Also Do these minsets forms a partition of A?
Answers
Given : A = {1,2,3,4,5,6,7,8,9}
B1 = {5,6,7} , B2 = {2,4,5,9} and B3 = {3,4,5,6,8,9}
To Find : minsets generated by B1, B2, and B3
Solution:
B1 = {5,6,7} , B2 = {2,4,5,9} and B3 = {3,4,5,6,8,9}
B1' = {1,2,3,4,8,9} B2'= {1,3,6,7,8} , B3' = {1, 2 , 7}
B1, B2, and B3 are 3 sets hence minsets generated = 2³ = 8
1 2 3 1 ∩ 2 ∩ 3
B1 B2 B3 5
B1 B2 B3' Ф
B1 B2' B3 6
B1 B2' B3' 7
B1' B2 B3 4 , 9
B1' B2 B3' 2
B1' B2' B3 3, 8
B1' B2' B3' 1
Union of all sets = {1,2,3,4,5,6,7,8,9}
Intersection of all sets = Ф
Hence these minsets forms a partition of A
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Find the minsets generated by B1, B2, and B3.
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