Sets Part 5

[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.

See attachment.

 

[Harry_the_cat]

What's your question?

 

[mathdad]

What's your question?

My question has been posted.

 

[Harry_the_cat]

I'll assume you want to know what that means

Find the set which is the intersection of A and B, then find the complement of that.

 

[HallsofIvy]

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

So what is \(\displaystyle A\cap B\)? That is, what is in both A and B? 1 is in A but not in B. 3 is in A but not in B. 4 is in both A and B! 5 is in A but not in B. 9 is in A but not in B.

So \(\displaystyle A\cap B= \{4\}\). The complement is all members of U that are not in that set..

 

[mathdad]

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

So what is \(\displaystyle A\cap B\)? That is, what is in both A and B? 1 is in A but not in B. 3 is in A but not in B. 4 is in both A and B! 5 is in A but not in B. 9 is in A but not in B.

So \(\displaystyle A\cap B= \{4\}\). The complement is all members of U that are not in that set..

See attachment.

 

[Dr.Peterson]

Correct.

 

[mathdad]

Correct.

Like Ron Howard once said on Happy Days: "I'm cooking with gas."