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#1 2024-09-08 02:22:42
- harpazo65
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- From: Brooklyn, NY
- Registered: 2024-09-07
- Posts: 52
Definition of Complement
Definition of complement states:
If A is a set, then the complement of A, denoted A^c, is the set consisting of all the elements in the universal set that are not in set A.
It follows that from the definition of complement that A U A^c = U, where U is the universal set. It also follows that A ∩ A^c = null set or Empty set.
Why is this the case?
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#2 2024-09-08 04:42:56
- Bob
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- Registered: 2010-06-20
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Re: Definition of Complement
A set and its complement divide the 'universe' into two non overlapping sets with no elements left out of being in one or the other. So when you unite them you get everything, ie the universe.
And when you look to find what's in both a set and its complement you find nothing hence the empty set.
Normally when I'm showing union and intersection in a picture I draw two overlapping circles (inside a rectangle for the universe). But for a set and its complement a better picture is a rectangle for the universe divided by a single border making the two sets that don't overlap and together make the whole of the universe rectangle.
Bob
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#3 2024-09-08 08:34:04
- harpazo65
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- From: Brooklyn, NY
- Registered: 2024-09-07
- Posts: 52
Re: Definition of Complement
A set and its complement divide the 'universe' into two non overlapping sets with no elements left out of being in one or the other. So when you unite them you get everything, ie the universe.
And when you look to find what's in both a set and its complement you find nothing hence the empty set.
Normally when I'm showing union and intersection in a picture I draw two overlapping circles (inside a rectangle for the universe). But for a set and its complement a better picture is a rectangle for the universe divided by a single border making the two sets that don't overlap and together make the whole of the universe rectangle.
Bob
I didn't know this information. This reply makes good study notes. I think set theory is worth exploring in the near future.
Focus on the journey for there will be those who would love to see you fall.
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