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Basics Definition From Set Theory
Here are some common definitions found in Set Operations:
- Complement: Is the set that contains all the elements that don't belong to an example set
S. This can be mathematically written as
S^c = U \ A
- Union: Is the combination of two sets such that all elements that belong to given sets
B(or both sets) are contained in the new set
A ∪ B
- Intersection: Is the combination of two sets such that only elements that belong to given sets
Bare contained in the new set
A ∩ B
- Disjoint: Is when two given sets do not have any elements in common. Therefore, their intersection would be empty
- Partition: Is when there is a set A and smaller sets within it that are all disjoint sets. In this scenario, the collection of smaller sets within set A can be said to be a partition of set A
- Sample space: Is the set of all possible outcomes of an experiment
- Probability law: Is a law of probability that assigns a nonnegative number, P, to a set A where the P represents our knowledge or belief about the collective probability of the elements of set A.
- Event: Is a subset of the sample space also known as a potential outcome from a set of possible outcomes
- Collectively Exhaustive: Is a probability related concept where at least one of the events in a given sample space must occur(or have a 100% probability)
- Mutually Exclusive: Is a probability related concept where two events cannot occur at the same time or simultaneously. This is also known as disjoint events
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