1) The symbols , , , ,  and  represent set membership, subset, null set, union, intersection, and not (complement) respectively. 2) C represents the set of all prime numbers between 10 and 20. n(C) represents the number of elements in set C. 3) A Venn diagram is constructed to represent sets U, A, B, and C where elements are filled in each region and used to find quantities such as n(A), n(B), n(C), n(B and C'), n(A and B and C), and n

1. Sets and Venn diagrams
1) What do the symbols , , , ,  and each mean?
2) Let C be "all prime numbers between 10 to 20". What is C? What is n(C)?
3) Construct a Venn diagram that satisfy the following:
U = {all integers between 1 to 30, inclusive}
A = {multiples of 2}
B = {multiples of 3}
C = {multiples of 5}
Fill in each of the 30 numbers into each region, and use your diagram to......
i) Find n(A), n(B) and n(C)
ii) Find n(B and C')
iii) Find A and B and C
iv) Find n((A or B) and (A or C))

2. 4) Shade the described region.
(A  B')  C' (A and C), or (A and not B) A'  (B'  C)
A'  C  B' (A'  B)'  C A  B  C'
5) Use set notations to describe the following shaded region. There could be more than 1 correct
answers:

3. 6. In Year 10 there are 80 students taking
anywhere from zero to three sciences:
40 students take all 3 sciences
45 students take chem and bio
6 students take only bio
54 students take bio
14 students take physics and chem but not bio
2 students don't do any science
The number of students that take only physics or
only chem are the same (x).
i) Use P, C and B to represent the group of physics, chemistry and biology students respectively,
draw the Venn diagram and calculate the value of x.
ii) Use your diagram to deduce......
n(C)
n(P  C)
n(P')
n(B'  C')
7. i) 30 primary school students are surveyed to see whether they like grumpy cat or doge or both.
20 students like grumpy cat, 24 students like doge and 1 student doesn't like either. How many students
like both?
ii) (lvl = Asian) 80 students were surveyed to see whether they like Coke, Sprite or Fanta:
33 students like Coke
24 students like Sprite
29 students like Fanta
9 students like only Sprite
12 students like Coke and Sprite
10 students like Fanta and Sprite
6 students like Coke and Fanta but not Sprite
x student like all 3 and y students dislike all 3
Find x and y.