if u={1,2,3,4,.......,10} is the universal set …
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Gaurav Seth 4 years, 5 months ago
If u equals to {1, 2, 3, 4,.....,10} is the universal set for the two sets a={2,3,4,5} and b={1,2,3,4,5,6} then verify that (a u b)" equals to a" n b"
Given
a = { 2, 3, 4, 5 } and b = { 1, 2, 3, 4, 5, 6 }
Then
a ∪ b = [ everything in one or the other ]
= { 1, 2, 3, 4, 5, 6 }
so
( a ∪ b )' = [ the complement, so everything in u that's not in a∪b ]
= { 7, 8, 9, 10 }. ...(*)
Also
a' = { 1, 6, 7, 8, 9, 10 } and b' = { 7, 8, 9, 10 }
so
a' ∩ b' = [ those elements in both a' and b' ]
= { 7, 8, 9, 10 }. ...(**)
The sets at (*) and (**) are the same, verifying the relationship
( a ∪ b )' = a' ∩ b'.
2Thank You