Complement of A Set

mathdad

mathdad

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It follows from the definition of a complement of a set that set A union with set A complement = universal set and set A intersected with set A complement = empty set. I don't understand why that is the case.
 
mathdad said:
It follows from the definition of a complement of a set that set A union with set A complement = universal set and set A intersected with set A complement = empty set. I don't understand why that is the case.
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Which of the two parts you don't understand? Which answers do you expect and why?
 
mathdad said:
It follows from the definition of a complement of a set that set A union with set A complement = universal set and set A intersected with set A complement = empty set. I don't understand why that is the case.
Click to expand...
Have you tried making an example? Suppose the universe is {a,b,c,d,e,f} and A = {b,c,f}. What is A'? What are the union and intersection? What does the example suggest in general?
 
Dr.Peterson said:
Have you tried making an example? Suppose the universe is {a,b,c,d,e,f} and A = {b,c,f}. What is A'? What are the union and intersection? What does the example suggest in general?
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I made an example using the 5 boroughs of NYC. Is my work correct?
 
Dr.Peterson said:
Have you tried making an example? Suppose the universe is {a,b,c,d,e,f} and A = {b,c,f}. What is A'? What are the union and intersection? What does the example suggest in general?
Click to expand...
See picture.
 

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mathdad said:
See picture.
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True, but that's not the problem you asked about, and the example I suggested:
mathdad said:
It follows from the definition of a complement of a set that set A union with set A complement = universal set and set A intersected with set A complement = empty set. I don't understand why that is the case.
Click to expand...
Dr.Peterson said:
Suppose the universe is {a,b,c,d,e,f} and A = {b,c,f}. What is A'? What are the union and intersection? What does the example suggest in general?
Click to expand...
Clearly I was referring to the union and intersection you asked about, namely of A and A'.

What you found is [imath]A\cup U=U[/imath] and [imath]A\cap U=A[/imath]. You didn't even use the complement.

Try again, and actually answer your question, rather than one you make up on the spot.
 
blamocur said:
See post #2.
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mathdad said:
It follows from the definition of a complement of a set that set A union with set A complement = universal set and set A intersected with set A complement = empty set. I don't understand why that is the case.
Click to expand...
I can picture set A as a circle inside a larger rectangle representing the universal set U. The complement of set A is everything outside the circle.

You say?

If I combine A and A' (union), does that cover the entire rectangle (U)?

If I look for elements in both A and A' (intersection), I will probably find nothing or empty as in empty or null set.

You say?
 
blamocur said:
Yes it does.

Why
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I found this online:

A set and its complement always equal the empty set because by definition, a complement contains all elements that are not in the original set, meaning there is no overlap between the two, resulting in an empty set when you try to combine them (i.e., their intersection is empty).

You say?
 
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