What is the Set Union formula for A ∪ B = A' ∪ B?

Thread starter khd_saleem
Start date May 29, 2012
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Sets Union

In summary, the union of sets A and B is a mathematical operation represented by the symbol ∪ or "union", which combines all elements from both sets to form a new set. The cardinality of the union is equal to the sum of the cardinalities of both sets minus the cardinality of their intersection. The union is different from the intersection as it includes all elements from both sets, while the intersection only includes common elements. The union can also be an empty set if there are no common elements between the two sets.

May 29, 2012

khd_saleem

(a u b)'=a' u b'

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May 29, 2012

mathman

Science Advisor

khd_saleem said:

(a u b)'=a' u b'

Wrong: (a∪b)' = a'∩b'

May 29, 2012

berkeman

Mentor

khd_saleem said:

(a u b)'=a' u b'

Welcome to the PF.

Please make an effort to ask clear questions when you start a thread here at the PF. It is not clear at all if you have a question, and what it would be. You did get a nice correction though.

1. What is the definition of "Union of Sets A and B"?

The union of sets A and B is a mathematical operation that combines all the elements of both sets to form a new set. It includes all the elements that are present in either set A or set B or both.

2. How is the union of sets A and B represented?

The union of sets A and B is represented by the symbol ∪ or "union". This symbol is placed between the two sets and is read as "A union B".

3. What is the cardinality of the union of sets A and B?

The cardinality of the union of sets A and B is equal to the sum of the cardinalities of both sets minus the cardinality of their intersection. In other words, it is the total number of unique elements present in both sets.

4. How is the union of sets A and B different from the intersection?

The union of sets A and B combines all the elements from both sets, while the intersection only includes the elements that are common to both sets. In other words, the union is a combination of both sets, while the intersection is the overlap between the two sets.

5. Can the union of sets A and B be an empty set?

Yes, the union of sets A and B can be an empty set if there are no common elements between the two sets. For example, if set A contains only odd numbers and set B contains only even numbers, their union would result in an empty set.