Question at position 2 A and B returned True. Which of the following must also be True?ABA or BAll of the aboveNone of the above

Question

Question at position 2 A and B returned True. Which of the following must also be True?ABA or BAll of the aboveNone of the above

BlackTom AI · Accepted Answer

The question states: 'Question at position 2 A and B returned True. Which of the following must also be True?' And the answer choices are: A, B, A or B, All of the above, None of the above.

First, consider option A: If A is true, that is given by the stem as true. So option A is a candidate that could be true because it directly reflects one of the premises.

Next, consider option B: If B is true, that is also given by the stem as true. Thus option B is likewise a candidate that could be true since it aligns with the stated information.

Now examine option 'A or B': If A is true (as given) or B is true (as given), the disjunction 'A or B' must be true because at least one of the operands is true, and in this case both are true. Therefore this option is necessarily true.

Then consider 'All of the above': For this to be true, every listed option must be true: A, B, A or B, and None of the above. We have established that A, B, and A or B are all true. The remaining question is the truth value of 'None of the above.' Since 'None of the above' would be true only if none of A, B, A or B, and All of the above were true, it contradicts the established truths. Therefore 'None of the above' is false, which is compatible with 'All of the above' being true because 'All of the above' asserts that all the other statements except itself are true, and indeed A, B, and A or B are true while None of the above is false. Consequently, the statement 'All of the above' accurately captures that all the other listed options (A, B, and A or B) are true, while None of the above is false.

Finally, evaluate 'None of the above': Since we have already determined that A, B, and A or B are true, the statement 'None of the above' cannot be true. This option is incorrect because it directly contradicts the known truth of the other options.

In summary, A is true because it reflects the given information, B is true for the same reason, A or B is true because at least one of A or B holds, None of the above is false because there are true statements among A, B, and A or B, and All of the above is true because it asserts that A, B, and A or B are true (while 'None of the above' is false).

Question at position 2 A and B returned True. Which of the following must also be True?ABA or BAll of the aboveNone of the above

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