Complement of A Set

[mathdad]

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.

 

[blamocur]

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.

Which of the two parts you don't understand? Which answers do you expect and why?

 

[Dr.Peterson]

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.

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?

 

[mathdad]

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?

I made an example using the 5 boroughs of NYC. Is my work correct?

 

[mathdad]

Which of the two parts you don't understand? Which answers do you expect and why?

See my example concerning the 5 boroughs of NYC.

 

[Dr.Peterson]

See my example concerning the 5 boroughs of NYC.

Do all that I suggested, not just the first bit, which I already knew you could do.

 

[mathdad]

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?

See picture.

 

[Dr.Peterson]

See picture.

True, but that's not the problem you asked about, and the example I suggested:

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.

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?

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]

See my example concerning the 5 boroughs of NYC.

I don't see how this answers my two questions.

 

[mathdad]

I don't see how this answers my two questions.

Sorry. What are the two specific questions that you want me to address?

 

[blamocur]

Sorry. What are the two specific questions that you want me to address?

See post #2.

 

[mathdad]

See post #2.

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.

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]

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

Yes it does.

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

Why "probably" ?

 

[mathdad]

Yes it does.

Why

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?