General
Set operations
Logical Sieve
100
Decide if the following collections are sets:
a) the best superhero
b) the countries of the world
c) the greatest showman
a) not a set
b) set
c) not a set
100
A = {1, 2, 3, 4}
B = {2, 4, 6, 8}
Define the intersection of A and B
A∩ B= {2, 4}
100
In a class 15 students like football, 12 like basketball and 6 like both. How many students are there in the class if 3 students do not like either?
24
200
Give the following set by listing its elements:
A = {the set of integers which are at least 10 and less than 20}
A= {10, 11, 12, 13, 14, 15 16, 17, 18, 19}
200
A = {one-digit prime numbers}
B = {one-digit odd numbers}
Give the union and intersection of these sets.
A = {2, 3, 5, 7}
B = {1, 3, 5, 7, 9}
A∩ B={3, 5, 7}
AUB = {1, 2, 3, 4, 5, 7, 9}
200
In a group of 12 friends, 8 people want to go to the cinema, 6 people want to go to a concert and 1 person doesn't want either. How many people want both?
3
300
A = {3, 4, 5}
List all the subsets of A. Which of these are proper subsets?
Subsets: {} {3} {4} {5} {3, 4} {4, 5} {3, 5} {3, 4, 5}
Each is a proper subset except the last one.
300
U = {integers at least 1 and at most 15}
A = {even numbers}
B = {numbers divisible by 5}
Define A' , (A∩ B)' and (AUB)'
A' = {1, 3, 5, 7, 9, 11, 13, 15}
(A∩ B)' = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15}
(AUB)' = {1, 3, 7, 9, 11, 13}
300
A sport association has 550 members. 20% of them either play handball or volleyball. 60 people play handball in the association and 25 people do both sports. How many people play volleyball?
75
400
What are the elements of the universe? What is the complement of the set of 'odd numbers'?
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,20}
{odd numbers}' = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
400
Who belongs in the set S'∩V? Who belongs in (SUT)\V?
S' = {Jade, Glen, Blair, Erin, Francis, Ira}
V = {Drew, Jade, Glen}
S'∩ V={Jade, Glen}
SUT={Alex, Hunter, Casey, Drew}
(SUT)\V={Alex, Hunter, Casey}
400
There are 17 students in a math group. 7 of them like AC /DC (set A), 8 like Black Sabbath (set B) and 6 like Miley Cyrus (C). 4 like both A and B, 2 like both B and C and 3 like both A and C. There is one student who likes all of them. How many people are there in the group who doesn't like any of these musicians?
4
500
How many subsets does the set A = {3, 4, 5, 6, 7} have?
25=32
500
Colour the correct parts of the Venn-diagram to represent these operations.
(A\B)∩ C
A∩ (BUC)'
U \ (A∩ B)
Look at the board.
500
In a music school each student can learn to play three types of instruments (everybody learns to play at least one). 43 students learn to play the violin, 46 learn to play the piano and 33 learn to play the flute. Nobody learns to play all three instruments. There are 27 students who learn to play exactly two instruments, 9 of them learn to play both the violin and the piano, 7 learn to play both the violin and the flute. How many learn to play only the flute? How many students are there in this school?
only the flute: 15
in the school: 95