The content of A1 is hidden from you. But, you know that a logical value was entered in that cell.

When you execute the following formula in A3, what would be the outcome returned in A3?

=OR(A1=TRUE,A1=FALSE)

Question

The content of A1 is hidden from you. But, you know that a logical value was entered in that cell.

When you execute the following formula in A3, what would be the outcome returned in A3?

=OR(A1=TRUE,A1=FALSE)

BlackTom AI · Accepted Answer

A logical cell contains either the boolean value TRUE or the boolean value FALSE, so one of the two comparisons in the OR expression must evaluate to TRUE.

1. Relevant knowledge points and concepts
- In spreadsheet logic, a cell that holds a logical value contains exactly TRUE or FALSE (boolean).
- The equality check A1=TRUE returns the boolean TRUE if A1 is TRUE, otherwise FALSE.
- Similarly A1=FALSE returns TRUE if A1 is FALSE, otherwise FALSE.
- The OR function returns TRUE if at least one of its arguments is TRUE; it returns FALSE only if every argument is FALSE.

2. Complete reasoning process step by step
- We evaluate the formula =OR(A1=TRUE, A1=FALSE). There are only two possible logical values that A1 can contain: TRUE or FALSE (by problem statement).
- Consider both possible cases separately.

3. Intermediate evaluation steps (case analysis)
- Case A: A1 contains TRUE.
  - A1=TRUE evaluates to TRUE.
  - A1=FALSE evaluates to FALSE.
  - OR(TRUE, FALSE) evaluates to TRUE.
- Case B: A1 contains FALSE.
  - A1=TRUE evaluates to FALSE.
  - A1=FALSE evaluates to TRUE.
  - OR(FALSE, TRUE) evaluates to TRUE.

4. Why the correct answer is correct
- In both exhaustive cases (A1 is TRUE or A1 is FALSE), the OR of the two comparisons yields TRUE because one of the two comparisons is guaranteed to be TRUE when A1 is a logical value. Thus the formula always returns TRUE under the given condition.

5. Why the other options are incorrect
- FALSE: impossible because for FALSE to be returned both comparisons would have to be FALSE, which would mean A1 is neither TRUE nor FALSE — contradicting the premise that a logical value was entered.
- "Not enough information": also incorrect because the premise specifies A1 contains a logical value, which is sufficient to determine the result as shown by the case analysis.

6. Conclusion
- The formula always evaluates to TRUE given that A1 contains a logical value. This matches the provided answer: TRUE.

The content of A1 is hidden from you. But, you know that a logical value was entered in that cell. When you execute the following formula in A3, what would be the outcome returned in A3? =OR(A1=TRUE,A1=FALSE) 单项选择题

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