1. The registrar reported that among 1400 students, 460 did not register for either a math or English course, 480 registered for an English course, and 325 registered for both types of courses.

Define the sets as follows:

= { | }, = { | h },

= { | h }

Using set notation, write in following sets:

1a. "Students who registered for a math course and an English course"

1b. "Students who registered for a math course and not an English course"

1c. "Students who registered for a math course or an English course"

1d. "Students who did not register for a math course or an English course"

Create a complete Venn diagram for the problem and use it to answer:

1e. How many students registered for an English course and not a math course?

1f. How many students registered for a math course?

2. A survey of 500 shoppers revealed that 124 purchased asparagus that day, 221 purchased broccoli that day and 195 purchased cauliflower that day. Of those surveyed, 85 of those surveyed purchased broccoli and cauliflower but not asparagus, 42 purchased asparagus and cauliflower but not broccoli, 75 purchased only broccoli, and 36 bought all three vegetables.

Create a complete Venn diagram for the problem and use it to answer the following:

2a. How many shoppers purchased only cauliflower?

2b. How many shoppers purchased asparagus and broccoli but not cauliflower?

2c. How many shoppers did not purchase any of the three vegetables?