Three sets divide the universal set into at most ___ regions.

a. How many subsets are there of the set {0, 1, 2, 3, ..., 10}? b. How many maps of this set into itself are one-to-one? c. How many maps of this set onto itself?

Find the indicated number of elements by referring to the table of enrollments in a finite mathematics class. Let the universal set U be the set of all 112 students in the​ class, A the set of students from the College of Arts​ & Sciences, B the set of students from the College of​ Business, F the set of​ freshman, and S the set of sophomores. Find the number of students in A∩F.   Question content area top right Part 1   Freshman Sophomores Arts​ & Sciences 16 14 Business 57 25     ​n(A∩F​)=enter your response here

Find the indicated number of elements by referring to the table of enrollments in finite math class. Let the universal set U be the set of all 109 students. A the students in College of Arts and Sciences, B the set of students from the College of business, F the set of freshmen and S the set of sophomores. Find the number of students in SUF Arts and sciences 15 freshmen, 10 sophomores Business 56 freshmen, 28 sophomores n(SUF) =

What are all the proper subsets for {a, b, c}?

Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly size 2 does A have? 2. How many subsets of at least size 2 does A have? 3. How many subsets of at most size 2 does A have?

Show that if B is a countable subset of an uncountable set A, then A-B is uncountable.

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