A guidance counselor is planning schedules for 40 students. 19 students want to take Algebra (A) 24 want to take Biology (B) 15 want to take Chemistry (C) 8 want Biology and Algebra 2 want Algebra and Chemistry, but not Biology 10 want Biology and Chemistry, but not Algebra 12 want Biology and Chemistry Remember: A = Algebra B = Biology C = Chemistry Fill in the number of students for each of the numbered areas (labeled in red)  Area 1                     Area 2 Area 3                     Area 4 Area 5                     Area 6 Area 7                     Area 8

Choose   YES or  NO   from the Dropdown Menu. Given      U = {c, h, e, m, i, s, t, r, y, l, a, b}  and    A = {m, e, a, t}             B = {b, i, s, t}          C = {s, t, r, e, a, m}      D = {c, h, i, m, e, s}     E= {t, e, a, m}   a. Is A = E ?    b. Is E ⊄ C ?   c. Is {m, e} ∈ C ?    d. Is B ~ E ?    e. Is E ⊆ A ?    f. Is m ∈ D ?    g. Is C ⊂ A ?    h. Is A ⊆ D ?   

If U = {x|x is all IUS students}    and   A= {x|x is a male IUS student}    and      B = {x|x is an IUS student majoring in business} then which of the following is the best description of :     

Given: n(A) = 15   and   n(B) = 23  a.   What is the minimum possible number of elements in A ∩ B?    b.   What is the maximum possible number of elements in A ∪ B?   

How many proper subsets does the following set have? T = {m, a, t, h, i, s, #, 1}  Express answer as a Natural Number 

List all the proper subsets of the set  G= {g, e, m} Be sure to write your answer using proper notation.

Given: n(A) = 15   and   n(B) = 23  a.   What is the maximum possible number of elements in A ∩ B?    b.   What is the minimum possible number of elements in A ∪ B?   

If  A = {1, 2}  and B = {x, y, z} ,  find the Cartesian product A × B. Be sure to write your answer using proper notation – using ( ) and { } correctly.

Karen asked 60 coffee drinkers whether they like cream and/or sugar in their coffee.  Twelve said they like both, twenty-nine said they like cream and eight said they like it black. HINT:  Draw a Venn Diagram to help solve the problem. a.  How many drinkers like only sugar in their coffee? b. How many drinkers do not like cream in their coffee? 

EXTRA CREDIT    (4 POINTS) If   , find a simpler expression for each of the following.   a.      b.