Operations involving set theory :
(i) Union
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B
(ii) Intersection
The intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.
(iii) Difference
The set which contains the elements which are either in set A or in set B but not in both is called the difference between two given sets.
(iv) Complementation
In set theory, the complement of a set A, often denoted by A^{c} (or A′), are the elements not in A. A circle filled with red inside a square.
Problem 1 :
Find the following in the venn diagram.
a) List : i) set C ii) set D iii) set U iv) set C ∩ D v) set C ∪ D |
b) Find : i) n(C) ii) n(D) iii) n(U) iv) n(C ∩ D) v) n(C ∪ D) |
Solution :
i) set C = {1, 3, 7, 9}
ii) set D = {1, 2, 5}
iii) set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
iv) set C ∩ D = {1}
v) set C ∪ D = {1, 2, 3, 5, 7, 9}
b)
i) n(C) = 4
ii) n(D) = 3
iii) n(U) = 9
iv) n(C ∩ D) = 1
v) n(C ∪ D)
n(C ∪ D) = n(C) + n(D) – n(C ∩ D)
= 4 + 3 – 1
= 6
Problem 2 :
Find the following.
i) set A ii) set B iii) set U iv) set A ∩ B v) set A ∪ B |
i) n(A) ii) n(B) iii) n(U) iv) n(A ∩ B) v) n(A ∪ B) |
Solution :
i) set A = {2, 7}
ii) set B = {1, 4, 6}
iii) set U = {1, 2, 3, 4, 5, 6, 7, 8}
iv) set A ∩ B = { }
v) set A ∪ B = {1, 2, 4, 6, 7}
b Find :
i) n(A) = 2
ii) n(B) = 3
iii) n(U) = 8
iv) n(A ∩ B) = { }
v) n(A ∪ B)
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 2 + 3 – {}
= 5
Problem 3 :
a) List the elements of :
i) U ii) N iii) M
b) What are n(N) and n(M)?
c) Is M ⊆ N?
Solution :
i) U = {1, 2,
3, 4, 5, 6, 7, 8, 9, 10}
ii) N = {8, 3}
iii) M = {1, 4, 7}
b) n(N) = 2 and n(M) = 3
c) M ⊆ N = {1, 3, 4, 7, 8}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM