Consider the statement: 'Some number in the set is positive and odd.' Which of the following is its negation?
Answer and explanation
Correct answer: B. Every number in the set is not positive or is even
- Step 1: The statement is ''. Its negation is ''.
- Step 2: By De Morgan, : every number is not positive or is even.
Answer
Every number in the set is not positive or is even.
Why not the others: 'No number is positive or odd' and 'every number is not positive and even' turn 'or' into 'and' at the wrong step; 'some ... and' and 'some ... or' keep 'some', but a negation of an existence claim must be universal.
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