1. Math 0332 Negations of Quantified Statements Name ______________
Negations and equivalences of quantified statements are given in the following diagram.
Each quantified statement’s equivalence is written in parenthesis below the statement.
The statement diagonally opposite each other are negatives.
All A are not B.
(There are no A that are not B.
No A are B.
(All A are not B.)
Some A are B.
(There exists at least one A that is a B.
Some A are not B.
(Not all A are B.)
The board of supervisors told us, “All new tax dollars will be used to improve education.”
I have learned that the board of supervisors never tells the truth.
Write the negation of the quantified statement. (The negation should begin with “all,” “some,” or “no.”
1. Some students are business majors.
What can I conclude?
Express the conclusion in two different ways.
Some new tax dollars will not be used to improve education.
At least one new tax dollar will not be used to improve education.

2. Exercise 1
Write the negation of the quantified statement.
Statements
All whales are mammals.
All journalist are business majors.
Exercise 2
Write the negation of the quantified statement.
Statements
Some movies are comedies.
Some thieves are not criminals.
Exercise 3
Write the negation of the quantified statement.
Statements
No Democratic presidents have been impeached.
No women have served as Supreme Court justices.
Exercise 4
Write the negation of the quantified statement.
Statements
There are no seniors who did not graduate.
There are no applicants who were not hired.
Exercise 5
Write the negation of the quantified statement.
Statements
Not all parrots are pets.
Not all dogs are playful.