If A = { 2,3,4,5,6} B = { 0,9,8,7} verify commutative property of set union and set intersection
Answers
Answer:
Step-by-step explanation:
Union of Sets
The union of two sets A and B is the set of elements, which are in A or in B or in both. It is denoted by A ∪ B and is read ‘A union B’
The following table gives some properties of Union of Sets: Commutative, Associative, Identity and Distributive. Scroll down the page for more examples.
Properties of Union of Sets
Example :
Given U = {1, 2, 3, 4, 5, 6, 7, 8, 10}
X = {1, 2, 6, 7} and Y = {1, 3, 4, 5, 8}
Find X ∪ Y and draw a Venn diagram to illustrate X ∪ Y.
Solution:
X ∪ Y = {1, 2, 3, 4, 5, 6, 7, 8} ← 1 is written only once.
If X ⊂ Y then X ∪ Y = Y. We will illustrate this relationship in the following example.
Example:
Given U = {1, 2, 3, 4, 5, 6, 7, 8, 10}
X = {1, 6, 9} and Y = {1, 3, 5, 6, 8, 9}
Find X ∪ Y and draw a Venn diagram to illustrate X ∪ Y.
Solution:
X ∪ Y = {1, 3, 5, 6, 8, 9}
Complement of the Union of Sets
The complement of the set X ∪Y is the set of elements that are members of the universal set U but are not in X ∪Y. It is denoted by (X ∪ Y ) ’
Example:
Given: U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
X = {1, 2, 6, 7} and Y = {1, 3, 4, 5, 8}
a) Draw a Venn diagram to illustrate ( X ∪ Y ) ’
b) Find ( X ∪ Y ) ’
Solution:
a) First, fill in the elements for X ∩ Y = {1}
Fill in the other elements for X and Y and for U
Shade the region outside X ∪ Y to indicate (X ∪ Y ) ’
b) We can see from the Venn diagram that
(X ∪ Y ) ’ = {9}
Or we find that X ∪ Y = {1, 2, 3, 4, 5, 6, 7, 8} and so
(X ∪ Y ) ’ = {9}
Step-by-step explanation:
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