Find the negation of the following statement: "There exists a negative real number z such that -3<f(z)<=0"

Wierzycaz

Wierzycaz

Answered question

2021-02-05

Find the negation of the following statement:
"There exists a negative real number z such that -3

Answer & Explanation

tafzijdeq

tafzijdeq

Skilled2021-02-06Added 92 answers

The negation of a statement is the opposite of the statement.
The given statement is "There exists a negative real number z such that 3<f(z)0."
The negation of the quantifier "There exist" is "For every".
Also negation of 3<f(z)0 is f(z)3orf(z)>0.
Therefore, the negation of the statement "There exists a negative real number z such that 3<f(z)0" is,
"For every negative real number z, we have f(z)3orf(z)>0".

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