Question

Is anyone good in finite math? and can answer questions 1-3

Answer 1

This is an exercise of operation between sets. This is the data we know:

`A={}{}\lbrace2,4,5,8\rbrace`

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:

`\begin{gathered} 1.X\\e0,Y\\e0 \\ 2.\text{ }X\cup Y=A \\ 3.\text{ }X\cap Y=0 \end{gathered}`

In this case, there are 7 distintic pairs of disjoint non-empty subsets of the set A and they are:

`\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}`