Sets Help!

Alphard said:

What is {1}-{0}? is it {1} \(\displaystyle Yes.\)

\(\displaystyle \text{Alphard, for all of the following, you never stated what}\)
\(\displaystyle \text{members are in the universal set, set A, set B, or set C.}\)


From analyzing your exercises here, suppose they are meant to be:

\(\displaystyle \text{U = \{0, 1, 2, 3, 4, 5}\}\)
\(\displaystyle \text{A = \{1, 2, 3}\}\)
\(\displaystyle \text{B = \{0, 1, 4}\}\)
\(\displaystyle \text{C = \{2, 4, 5}\}\)


Based on these, I am answering as follows:

And please check these:
1)(A'-B)'
({0,4,5}) - {0,1,4})'
({5})'
= {0,1,2,3,4}
\(\displaystyle \text{Yes.}\)


2) (A?B)-(AUC)'
({1}) - ({1,2,3,4,5})'
{1}-{0}
= {1}
\(\displaystyle \text{Yes.}\)


3) [(A-B)' - C]'
[({0,2,3,4})' - C]'
[({1,5})- {2,4,5}]'
[{1}]'
= {0,2,3,4,5}
\(\displaystyle \text{A - B = \{2, 3\}, so (A - B)' = \{0, 1, 4, 5\}}\)
\(\displaystyle \text{Continue with that.}\)


4)
(A?C)? B'
({2})?{2,3,5}
= {2}
\(\displaystyle \text{Yes.}\)


5) (A-B')' - C'
({1,2,3} - {2,3,5})' - C'
({1,5})' - C'
{0,2,3,4} - {0,1,3}
= {2,4}
\(\displaystyle \text{\{1, 2, 3\} - \{2, 3, 5\} = \{1\}}\)
\(\displaystyle \text{Continue with that.}\)


6)
(A?U)' - B
({1,2,3})' - B
{0,4,5} - {0,1,4}
= {5}
\(\displaystyle \text{Yes.}\)


Are they correct?

Click to expand...