Quiz April Sections 1.6,1.7,1.8,4.1,4.2

Quiz: Apr. 20 ’04: pm 1.Set S1 is the set of all Irish citizens with blue eyes. Set S2 is the set of all Irish citizens with black hair. Set S3 is the set of all Irish citizens. |S1| = 1000, |S2|=3000, |S3|=10,000, a. Draw a Venn diagram for S1, S2, S3 with U = set of all living people. b. What is the total number of Irish citizens with blue eyes AND black hair. c. What is the total number of Irish citizens with blue eyes OR black hair. (inclusive OR). d. What is the total number of Irish citizens with blue eyes OR black hair, but not both? (exclusive OR). e. What is the total number of Irish citizens that do NOT have blue eyes. f. What is the total number of Irish citizens that do NOT have blue eyes AND do NOT have black hair. g. What is the total number of Irish citizens that do NOT have blue eyes OR do NOT have black hair. (inclusive OR). h. We define the mapping from S1 U S2 to S3, where each Irish citizen in S1 U S2 is mapped to the corresponding person in S3. Is this mapping 1) one-to-one, 2) onto, 3) a one-to-one correspondence?

Answers Quiz U S1 S2 a) Venn diagram b) 200 c) = 3800 d) ( ) + ( ) = 3600 S3 e) 10,000 – 1000 = 9000 f) 10,000 – 3800 = 6200 g) 10,000 – 200 = 9800 h) one-to-one: yes. (every member of S3 gets only one incoming arrow) onto: no. (Not all Irish citizens are reached by the mapping. one-to-one correspondence: no (not onto).