Final answer:
To show that a ∪ b ∪ c is an event, we need to prove that it satisfies the properties of an event. This can be done by considering the union of two events, a and b, and extending it to three events, a ∪ b ∪ c.
Step-by-step explanation:
To show that a ∪ b ∪ c is an event, we need to prove that it satisfies the properties of an event. An event is a subset of the sample space, which means it consists of outcomes of an experiment.
First, let's consider the union of two events, a and b. The union of a and b is denoted as a ∪ b and includes all outcomes that are in a or in b, or in both. Since a and b are events, they are subsets of the sample space. So, any outcome that is in a or in b, or in both, is still within the sample space, and therefore a ∪ b is also a subset of the sample space, making it an event.
Now, to extend this to three events, let's consider the union of a, b, and c, denoted as a ∪ b ∪ c. This union includes all outcomes that are in a, or in b, or in c, or in any combination of the three events. Since a, b, and c are all events, and events are subsets of the sample space, any outcome that falls within any of these events or their combinations still falls within the sample space, and therefore a ∪ b ∪ c is also a subset of the sample space, making it an event.
1