What Disjoint sets is
Disjoint sets are sets in which the elements have no common element. In other words, the elements of one set have no relation to the elements of another set. This type of set is also referred to as mutually exclusive or disjoint sets.
Steps for Disjoint Sets:
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Identify the elements of the sets. Each set should contain distinct elements that have no common elements.
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Determine the relationship between the sets. If the sets are disjoint, then the elements of one set are not related to the elements of the other set.
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Draw a Venn diagram to represent the disjoint sets. The diagram should have two circles that do not intersect.
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Label the circles with the appropriate set names.
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Place the elements of each set within its respective circle.
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Verify that the sets are mutually exclusive by confirming that no elements appear in both circles.
Examples
- Computing the probability of two events being independent of each other by using the concept of disjoint sets.
- Calculating the probability of two mutually exclusive outcomes, such as heads and tails in a coin toss.
- Determining the probability of a random variable taking on a particular value given that it is known to take on one of two mutually exclusive outcomes.
- Estimating the probability of two or more events occurring simultaneously by using the concept of disjoint sets.
- Determining the probability of two or more mutually exclusive outcomes, such as the sun rising in the east or the west.