Sets 2

[harpazo]

College Algebra
Michael Sullivan
Section R.1
Real Numbers

Sets 2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set.

14. Find (A∩B) U C.

Solution:

(A∩B) U C = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8} U {1, 3, 4, 6}

(A∩B) U C = { 4 } U {1, 3, 4, 6}

(A∩B) U C = {1, 3, 4, 6}

Can we say that set C =
(A∩B) U C ?

Is this right?

If C is a set, the complement of C, denoted C', is the set consisting of all the elements in the universal set that are not in C.

16. Find C'.

C' = {0, 2, 5, 7, 8, 9}

Is this correct?

Note: Sets 3 will be posted tomorrow.

 

[pka]

College Algebra
Michael Sullivan
Section R.1
Real Numbers

Sets 2

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set.

14. Find (A∩B) U C.

Solution:

(A∩B) U C = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8} U {1, 3, 4, 6}

(A∩B) U C = { 4 } U {1, 3, 4, 6}

(A∩B) U C = {1, 3, 4, 6}

Can we say that set C =
(A∩B) U C ?

Is this right?

If C is a set, the complement of C, denoted C', is the set consisting of all the elements in the universal set that are not in C.

16. Find C'.

C' = {0, 2, 5, 7, 8, 9}

Is this correct?

Note: Sets 3 will be posted tomorrow.

All correct, well done.

 

[harpazo]

All correct, well done.

Wonderful. This means I understand the section on sets thus far.

 

[ksdhart2]

Can we say that set C = (A∩B) U C ?

For these specific sets \(A\), \(B\), and \(C\), yes, we have the relationship \(\displaystyle C = \left( A \cap B \right) \cup C\). However, I should caution that this relationship is not a general property of sets.

 

[harpazo]

For these specific sets \(A\), \(B\), and \(C\), yes, we have the relationship \(\displaystyle C = \left( A \cap B \right) \cup C\). However, I should caution that this relationship is not a general property of sets.

Yes, of course. I meant to say that
set C = (A∩B) U C for this particular problem.

 

[ksdhart2]

Sure. I figured as much, but I wanted to be sure to cover all my bases