In this article, you will get a quiz on the associative property of union between three sets for beginners. Before the quiz, we will learn about the associative property of union.
Associative Property of Union
The associative property states that there is no change in the result if you change the order of grouping the two sets within parentheses.
Mathematically Representation
For any sets A, B, and C
A ∪ ( B ∪ C ) = ( A ∪ B ) ∪ C
Example
Let set A={a,b} and set B={b,c,d} and C = {a,c}
Then,
B ∪ C = {b,c,d} ∪ {a,c}
= {a,b,c,d}
A ∪ ( B ∪ C ) = {a,b} ∪ {a,b,c,d}
A ∪ ( B ∪ C ) = {a,b,c,d}
Now, if we change the order of the sets, there is no change in the result. This is actually the associative property of union.
A ∪ B = {a,b} ∪ {b,c,d}
= {a,b,c,d}
( A ∪ B ) ∪ C = {a,b,c,d} ∪ {a,c}
( A ∪ B ) ∪ C = {a,b,c,d}
So, A ∪ ( B ∪ C ) = ( A ∪ B ) ∪ C
Quiz on the Associative Property of Union Between Sets
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