Difficulty: Easy

Average Score: 79%

If the television is off, then the children are playing outside. Which statement is logically equivalent?

Rationale

If the children are not playing outside then the television is off.

This statement is logically equivalent to the original conditional statement due to the principle of contraposition, which asserts that if the original statement is true, its contrapositive is also true.

A (If the television is not off then the children are not playing outside) YOUR ANSWER

This statement represents the inverse of the original conditional, which is not logically equivalent. The truth of the original statement does not guarantee the truth of its inverse; the television being off does not necessarily imply the children are not playing outside.

C (If the children are playing outside then the television is off) YOUR ANSWER

This statement is the converse of the original conditional statement. While it may seem plausible, the original statement does not imply that the children playing outside requires the television to be off. Thus, the converse is not logically equivalent.

D (If the children are not playing outside then the television is not off) YOUR ANSWER

This statement is also an incorrect representation, as it indicates a direct relationship that does not follow from the original conditional. The television could be off while the children are still indoors, making this statement logically flawed.

Conclusion

Logical equivalence in conditional statements is crucial for understanding implications in reasoning. The correct equivalent statement, "If the children are not playing outside then the television is off," captures the contrapositive aspect of the original statement, ensuring that the logical structure remains intact. Understanding these relationships aids in clearer reasoning and effective argumentation.

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