For an integer , the statement is *' is even or '*. Which of the following is its negation?
Answer and explanation
Correct answer: C. is odd and
- Step 1: By De Morgan's law, .
- Step 2: 'Not even' is 'odd' and 'not greater than 10' is '', so the negation is ' is odd and '.
Answer
is odd and .
Why not the others: 'Odd or ' changes the 'and' of De Morgan's law into 'or'; 'even and ' is the conjunction of the original parts; 'odd and ' negates only one part; the implication is not equivalent to the negation.
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