Sets Part 3

[mathdad]

Let U = universal set

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1, 3, 4, 5, 9}

B = {2, 4, 6, 7, 8}

C = {1, 3, 4, 6}

Find the set given A^c.

I understand that A^c (also expressed as an upper case letter A with a bar on top) to mean the complement of set A.

Textbook Definition:

If A is a set, the complement of A is the set consisting of all the elements in the universal set U that are not in A.

So, in light of this definition,
my answer is A^c = {2, 4, 6, 8}.

Correct?

 

[Harry_the_cat]

No have another go. Your definition is correct.

 

[mathdad]

No have another go. Your definition is correct.

I forgot the number 0.

A^c = {0, 2, 4, 6, 8}

 

[Harry_the_cat]

Still not correct. 4 is in set A, so is not in the complement of A.

Look at Set U, cross out all the elements that are in A, what's left will be the complement of A.

Have another go.

 

[mathdad]

Still not correct. 4 is in set A, so is not in the complement of A.

Look at Set U, cross out all the elements that are in A, what's left will be the complement of A.

Have another go.

One more try, right?

A^c = {0, 2, 6, 7, 8}

 

[pka]

Let U = universal set

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 3, 4, 5, 9}
B = {2, 4, 6, 7, 8}
C = {1, 3, 4, 6}
Find the set given A^c.
I understand that A^c (also expressed as an upper case letter A with a bar on top) to mean the complement of set A.
Textbook Definition: If A is a set, the complement of A is the set consisting of all the elements in the universal set U that are not in A.
So, in light of this definition,
my answer is A^c = {2, 4, 6, 8}.
Correct?

Note that the common part of a set and its complement is empty: \(\displaystyle A\cap\overline{A}=\emptyset\).

 

[mathdad]

Note that the common part of a set and its complement is empty: \(\displaystyle A\cap\overline{A}=\emptyset\).

Ok but is my answer correct?

 

[Dr.Peterson]

One more try, right?

A^c = {0, 2, 6, 7, 8}

Yes, that's correct.

The comment about the intersection was probably intended to show how to check your answer, as your previous answers would have failed that check. But the easiest way to get the answer is, as was said, to copy U, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} , and then cross off the elements of A (at least in your head): {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} .

 

[mathdad]

Yes, that's correct.

The comment about the intersection was probably intended to show how to check your answer, as your previous answers would have failed that check. But the easiest way to get the answer is, as was said, to copy U, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} , and then cross off the elements of A (at least in your head): {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} .

Great! Another one for the study files.