Question

4. X = {10, 20, 30, 40} and Y = {1,2,3,4}. X Y (a) Copy and complete the Venn diagram. (b) List the elements of XU Y. (C) List the elements of X n Y. (d) What is #(XU Y)? (e) What is #(X n Y)?

Answer 1

At first, let us complete the digram

a)

b)

$X\cup Y$

Means write all the elements in X and Y, then

$X\cup Y=\mleft\lbrace1,\text{ 2, 3, 4, 10, 20, 30, 40}\mright\rbrace$

c)

$X\cap Y$

Means write the common elements in X and Y

Since there are no common elements in X and Y, then

$\begin{gathered} X\cap Y=\mleft\lbrace \mright\rbrace \\ OR \\ X\cap Y=\emptyset \end{gathered}$

d)

The number of elements in

$X\cup Y$

is 4 + 4 = 8 elements

#(XUY) = 8

e)

The number of elements in

$X\cap Y$

is zero because there are no common elements between X and Y

#(XnY) = 0