Question

Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If xED, then xEW. Choose the correct answer below. A. The statement is true. B. The statement is false. It can be changed to "if xEW, then xED." C. The statement is false. It can be changed to "If xEW, then xED." D. The statement is false. It can be changed to "If xEW, then xD." E. The statement is false. It can be changed to "If xED, then xW." F. The statement is false. It can be changed to "if xEW, then xD." G. The statement is false. It can be changed to "If xED, then xEW."

Answer 1

The correct answer is D. The statement is false. It can be changed to "If xEW, then xD."

Step-by-step explanation:

The original statement asserts, "If xED, then xEW," which is a false statement. To correct it, we need to switch the positions of "D" and "W" in the statement. The corrected version should read, "If xEW, then xD," making answer D the correct choice.

In the corrected statement, the implication is that if x belongs to the set of events W, then x also belongs to the set of events D. This adjustment aligns with logical reasoning and makes the statement true. It is important to note that the change involves swapping the positions of "ED" and "EW" to accurately reflect the logical relationship between the two events.

In symbolic logic, the corrected statement can be represented as follows: "If x∈W, then x∈D," where "∈" denotes membership in a set. This adjustment adheres to the principles of logical reasoning, ensuring that the statement accurately conveys the relationship between the two sets of events.