The lamp is on if and only if the switch is up. Which of the following says the same thing?
Answer and explanation
Correct answer: A. Either both the lamp is on and the switch is up, or neither is the case
- Step 1: 'If and only if' means and : the two statements always have the same truth value.
- Step 2: So either both are true or both are false.
Answer
Either both the lamp is on and the switch is up, or neither is the case.
Why not the others: 'Both true' alone omits the case where both are false; 'or' allows exactly one to be true; 'if on then up' is only one direction; 'exactly one' is the opposite of the biconditional.
Practise more Implications, converses and negations.
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More Implications, converses and negations questions
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