Question

Determine whether "C," "C," both, or neither can be placed in the blank to make the statement true:

{x ∣ x is an even natural number between 0 and 3.
Choose the correct answer below:
A) Only "C"
B) Only "C"
C) Both "C" and "C"
D) None of the above

Answer 1

The events C and E are not mutually exclusive because the number 3 belongs to both sets. Thus, the answer to whether "C," "C," both, or neither can be placed in the blank to make the statement true is D) None of the above.

Step-by-step explanation:

The student is asking whether the events C and E are mutually exclusive. Event C consists of the odd numbers greater than two, which are {3, 5}. Event E includes all numbers less than five, which are {1, 2, 3, 4}. The intersection of event C and event E is not empty since they both contain the number 3. Hence, events C and E are not mutually exclusive because they can occur simultaneously - specifically the outcome of 3 is included in both events C and E.

To answer the student's original question, neither "C" nor "C" can be placed in the blank to make the statement true, since the events are not mutually exclusive. So, the correct answer is D) None of the above.