Consider the statement: 'Some player in the tournament beat every other player.' Which of the following is its negation?
Answer and explanation
Correct answer: D. Every player failed to beat at least one other player
- Step 1: The statement is 'there is an such that for every other , beat '.
- Step 2: Its negation swaps the quantifiers and negates the inner claim: 'for every there is some other that did not beat'.
Answer
Every player failed to beat at least one other player.
Why not the others: 'No player beat any other' is much stronger than needed; 'some player lost to everyone' is a different relation; 'every player beat at least one' is compatible with the original; 'some player beat nobody' can be true even when another player beat everyone.
Practise more Negating statements with quantifiers.
Free questions with an explanation for every one, and full timed TMUA mock tests.
More Negating statements with quantifiers questions
- Consider the statement: 'Everyone in the group knows at least one member of the group.' Which of the following is its negation?
- Consider the statement: 'Every integer in the list is positive or even.' Which of the following is its negation?
- Consider the statement: 'There is someone in the room who is liked by everyone in the room.' Which of the following is its negation?
- Consider the statement: *'For every positive integer , there is a prime number with .'* Which of the following is its negation…
- Consider the statement: 'No number in the set is prime.' Which of the following is its negation?
- Consider the statement: 'Every even number in the list is greater than 10.' Which of the following is its negation?