Grade Six Mathematics
Exercise 2
1. P = { 2, 3, 5, 7, 11}
Q= {4, 6, 8, 10, 12}
R= {5, 7, 9, 11}
2. The disjoint sets are sets P and Q and sets Q and R. 3. No set is a subset of another
Exercise 3
1. Prime Numbers 3. Square Numbers 5. Even numbers 2. Odd numbers 4. Multiples of 5 6. Whole numbers
Exercise 4
= {1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18} - 12 elements E’ = {1, 9, 25, 49} – 4 elements
Exercise 5
1. (a) X = {2,4,6,8} 2. (a) X∩Y = { } (b) Y= {1,3,5,7} (b) X∩Z = {6} (c) Z= {3,6,9} (c)Y∩Z ={3}
Hello Boys and Girls!
I hope that you continue to follow the COVID-19 guidelines. Let’s continue learning about Sets.
Union of Sets
The union of two given sets is the smallest set which contains all the elements of both sets.
The symbol for denoting the union of sets is ‘U’.
For example;
Let set A = {2, 4, 5, 6} and set B = {4, 6, 7, 8}
Taking every element of both the sets A and B, without repeating any element,we get a new set = {2, 4, 5, 6, 7, 8}.
This new set contains all the elements of set A and all the elements of set B with no repetition of elements and is named as union of set A and B or written as A U B = {2, 4, 5, 6, 7, 8}.
Solved examples to find union of two given sets:
1. If A = {1, 3, 7, 5} and B = {3, 7, 8, 9}. Find union of two set A and B. Solution:
A U B = {1, 3, 5, 7, 8, 9}
No element is repeated in the union of two sets. The common elements 3, 7 are taken only once.
2. Let X = {a, e, i, o, u} and Y = {ф}. Find union of two given sets X and Y.
Solution:
X U Y = {a, e, i, o, u}
Therefore, the union of any set with an empty set is the set itself.
3. If set P = {2, 3, 4, 5, 6, 7}, set Q = {0, 3, 6, 9, 12} and set R = {2, 4, 6, 8}.
(i) Find the union of sets P and Q
(ii) Find the union of two set P and R
(iii) Find the union of the given sets Q and R
Solution:
(i) Union of sets P and Q is P U Q.
The smallest set which contains all the elements of set P and all the elements of set Q is {0, 2, 3, 4, 5, 6, 7, 9, 12}.
(ii) Union of two set P and R is P U R.
The smallest set which contains all the elements of set P and all the elements of set R is {2, 3, 4, 5, 6, 7, 8}.
(iii) Union of the given sets Q and R is Q U R.
The smallest set which contains all the elements of set Q and all the elements of set R is {0, 2, 3, 4, 6, 8, 9, 12}.
Exercise 1
Given that
A = {3,5,7}
C = {4,5,6,7}
E = {2,4,6,8,10}
B = {2,5,8,11} D = {1,4,5}
F = {1,5,9}
List all the elements in each of the following: 1.AUB 2.AUC 3. A U D
4.AUE 5.AUF 6. B U C
7.BUD 8.BUE 9. B U F
10. D U E 11. D U F 12. E U F
Venn Diagrams
A Venn Diagram is a picture representing one or more sets. It is made up of a rectangle which represents the universal set and circles which represent each set.
Each set is a subset of its universal set.
Venn Diagrams can be represented using three patterns. They are: