This is an exercise of operation between sets. This is the data we know:
[tex]A={}{}\lbrace2,4,5,8\rbrace[/tex]
Part a)
B = {4}
We must find a subset C such that B ∩ C = 0, and B ∪ C = A. In other words, we can say that C = A - B. Using Venn diagrams we see that C = {2,5,8}:
(Here is an image of the exercise)
Part b)
D = {2,8}
We must find a subset E such that D ∩ E = 0, and D ∪ E = A. In other words, we can say that E = D - A. Using Venn diagrams we see that E = {4,5}
Here is an image:
Part c)
X and Y are said to be distintic pairs of disjoint non-empty subsets of the set A if the followings are true:
[tex]\begin{gathered} 1.X\ne0,Y\ne0 \\ 2.\text{ }X\cup Y=A \\ 3.\text{ }X\cap Y=0 \end{gathered}[/tex]
In this case, there are 7 distintic pairs of disjoint non-empty subsets of the set A and they are:
[tex]\begin{gathered} 1.\text{ X=\textbraceleft2\textbraceright, Y = \textbraceleft4,5,8\textbraceright} \\ 2.\text{ x =\textbraceleft4\textbraceright, y = \textbraceleft2,5,8\textbraceright} \\ 3.\text{ x = \textbraceleft5\textbraceright, y = \textbraceleft2,4,8\textbraceright} \\ 4.\text{ x = \textbraceleft8\textbraceright, y = \textbraceleft2,4,5\textbraceright} \\ 5.\text{ x = \textbraceleft2,4\textbraceright, y = \textbraceleft5,8\textbraceright} \\ 6.\text{ x = \textbraceleft4,5\textbraceright, y = \textbraceleft2,8\textbraceright} \\ 7.\text{ x =\textbraceleft2,5\textbraceright, y = \textbraceleft4,8\textbraceright} \end{gathered}[/tex]
