Math 0332 Quantified Statements Name ________________________ Key Terms All Some No (or none) Quantifiers Quantified Statements. In English, we frequently encounter statements containing the words all, some and no( or none). These words are called quantifiers. A statement that contains one of these words is called a quantified statement. Statement An Equivalent Way to Express the Statement Example (Two Equivalent Quantified Statements All A are B There is no A that are not B. All poets are writers. There are no poets that are not writers. Some A are B There exists at least one A that is a B. Some people are bigots. At least one person is a bigot. No A are B All A are not B. No common colds are fatal. All common colds are not fatal. Some A are not B. Not all A are B. Some students do not work hard. Not all students work hard.

Math 0332 Quantified Statements Name ________________________ In English, we frequently encounter statements containing the words all, some and no( or none). These words are called quantifiers. A statement that contains one of these words is called a quantified statement. Exercise 1 All whales are mammals. All journalist are business majors. Equivalent Statements Statements Exercise 2 Some movies are comedies. Some thieves are not criminals. Equivalent Statements Statements Exercise 3 No Democratic presidents have been impeached. No women have served as Supreme Court justices. Equivalent Statements Statements Exercise 4 There are no seniors who did not graduate. There are no applicants who were not hired. Equivalent Statements Statements Exercise 5 Not all parrots are pets. Not all dogs are playful. Equivalent Statements Statements