Quantifiers And Negation

Step 1: Identify the original statement.
The original statement is: $%5Cexists%20n%20%5Cin%20%5Cmathbb%7BN%7D%20%5Ctext%7B%20such%20that%20%7D%20n%20%2B%208%20%3E%2011$ This means that there exists a natural number $n$ such that $n%20%2B%208%20%3E%2011$ , or equivalently, $n%20%3E%203$ .

Step 2: Negate the statement.
The negation of an existential statement ( $%5Cexists$ ) becomes a universal statement ( $%5Cforall$ ). Thus, the negation of the original statement is: $%5Cforall%20n%20%5Cin%20%5Cmathbb%7BN%7D%2C%20%5C%3B%20n%20%2B%208%20%5Cleq%2011$ Or equivalently, $%5Cforall%20n%20%5Cin%20%5Cmathbb%7BN%7D%2C%20%5C%3B%20n%20%5Cleq%203$

Final Answer: $%5Cforall%20n%20%5Cin%20%5Cmathbb%7BN%7D%2C%20%5C%3B%20n%20%5Cleq%203$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Quantifiers And Negation

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs