1. Define the sets A= {x|x is a letter in the phrase "i like math a lot"},
B= { x|x is a letter in the phrase "i like my math class"). and the universal set
U = {x|x is a letter in the alphabet} . Find:
(a). A ∪ B
(b). A ∩ B
(c). A' ∩ B
(d). true or false: a ∈ A
(e). true or false: Φ ∈ B
2. If n(A)= 18 , n(13)= 13, n(A ∩ B) = 9 and n(U)-= 50 , find:
(a). n(A ∪ B)
(b). n(A' ∩ B)
3. 100 people in the B/CS area are surveyed and asked which paper they take. 60 indicated they took the Houston Chronicle, 35 said they took the Dallas Morning News and 30 said they took the B/CS Eagle. 17 said they took both the Chronicle and the Eagle, 12 said they took the Chronicle and the News, 15 said they took the Eagle and the News and 7 said they took all 3 papers.
(a). Draw a Venn diagram to represent the relationships in this problem and define the basic sets you are representing.
(b). How many subscribed to only one paper?
(c). How many subscribed to none of the papers?
(d). How many took at least 2 of the papers?