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Two events that cannot happen at the same time are said to be mutually exclusive.
Not mutually exclusive, see solution.
We are asked whether the events of choosing a complex number and choosing a natural number are mutually exclusive. First, let's recall the definition of mutually exclusive events.
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Two events that cannot happen at the same time are said to be mutually exclusive. |
Now, let's suppose that we are choosing from the following numbers.
Recall that natural numbers form a subset of complex numbers. Notice that the first number 1+0* i is a complex number and also a natural number because 1+0* i=1, which is a natural number. Therefore, if we choose the first number we will choose a complex number and a natural number.
This means that the events of choosing a complex number and choosing a natural number can happen at the same time. Thus, the events are not mutually exclusive.