In which situation is the statement 'If the alarm sounds, then everyone leaves the building' false?
Answer and explanation
Correct answer: C. The alarm sounds and someone stays in the building
- Step 1: An implication is false only when is true and is false.
- Step 2: Here that is: the alarm sounds but not everyone leaves, i.e. someone stays in the building.
Answer
The alarm sounds and someone stays in the building.
Why not the others: If the alarm does not sound, the statement makes no promise, so it cannot be broken; if the alarm sounds and everyone leaves, the promise is kept; 'the alarm sounds if and only if someone stays in the building' is a different, more complicated claim that also includes the case where the alarm is silent.
Practise more Implications, converses and negations.
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More Implications, converses and negations questions
- Consider the statement: 'If a whole number is divisible by 6, then it is divisible by 3.' Which of the following is its contrapositive?
- Consider the statement: 'If a quadrilateral is a square, then all four of its sides are equal.' Which of the following is its converse?
- Which of the following is the negation of the statement 'If it rains, then the match is cancelled'?
- For an integer , the statement is *' is even or '*. Which of the following is its negation?
- Which of the following is the negation of *''*, where is a real number?
- Which of the following means the same as 'You can vote only if you are registered'?