Sets 3

[harpazo]

College Algebra
Michael Sullivan
Section R.1
Real Numbers

Sets 3

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.

See attachment for each question/solution.

 

[pka]

College Algebra
Michael Sullivan
Section R.1
Real Numbers

Sets 3

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.

See attachment for each question/solution.

View attachment 13116

Yes that answer is correct \(\displaystyle \overline{A\cap B}=\overline{A}\cup\overline{ B}\)
\(\displaystyle \overline{A\cup B}=\overline{A}\cap\overline{ B}\)

 

[HallsofIvy]

First, \(\displaystyle \overline{B\cup C}\) is NOT "two sets united under one line". \(\displaystyle B\cup C\) is itself a single set. Given that B= {2, 4, 6, 7, 8} and C= {1, 3, 4, 6} then \(\displaystyle B\cup C= \{1, 2, 3, 4, 6, 7, 8\}\).

\(\displaystyle \overline{B\cup C}= \{0, 5, 9\}\).

 

[harpazo]

Thank you everyone for your input and help.

 

[harpazo]

First, \(\displaystyle \overline{B\cup C}\) is NOT "two sets united under one line". \(\displaystyle B\cup C\) is itself a single set. Given that B= {2, 4, 6, 7, 8} and C= {1, 3, 4, 6} then \(\displaystyle B\cup C= \{1, 2, 3, 4, 6, 7, 8\}\).

\(\displaystyle \overline{B\cup C}= \{0, 5, 9\}\).

 

[HallsofIvy]

I would NOT call the intersection of two sets "uniting" them. That would be better used of the union.