FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.9(iii) Null, as there exists no positive number less than zero.
Example 5 : State with reasons whether each of the following statements is true or false :
(i) {1} ∈ {1,2, 3}, (ii) 1∈ {1, 2, 3 }, (iii) {1} ⊂ {1, 2, 3 }
Solution:
(i) False, {1} is a singleton and not an element of {1, 2, 3}
(ii) True, since 1 is an element and belongs to {1, 2, 3}
(iii) True, {1} is a proper sub-set of {1, 2, 3}
Example 6 : Let A = { 1, 3, {1}, {1, 3}, find which of the following statements are correct :
(i) {3} ∈ A , (ii) {3} ⊂ A, (iii) {{1}} ∈A
Solution:
(i) Incorrect as the set {3} is not an element of A.
(ii) Correct as the set {3} is a subset of A.
(iii) Incorrect as the set {{1}} is not an element of A.
Example 7 : A = {1, 2, 3, 4, 6, 7, 12, 17, 21, 35, 52, 56}, B and C are subsets of A such that B = {odd numbers},
C = {prime numbers}.
List the elements of the set { x : x ∈ B ∩ C}.
Solution:
B ∩ C = {1, 3, 7, 17, 21, 35} ∩ {2, 3, 7, 17} = {3, 7, 17} ∴ reqd. list = {3, 7, 17}
Example 8 : If S be the set of all prime numbers and M = {0, 1, 2, 3}, find S ∩ M.
Solution:
S = { 2, 3, 5, 7, 11, ....}, M = { 0, 1, 2, 3}; S ∩ M = {2, 3}
Example 9 : If A = { 1, 2, 3, 4, 5}, B = {2, 4, 5, 8}, C = {3, 4, 5, 6,7}, find A ∪ (B ∪ C).
Solution:
B ∪ C = { 2, 3, 4, 5, 6, 7, 8}, A ∪ (B ∪ C) = {1, 2,.........., 7, 8}
Example 10 : If A = {1, 2, 3}, and B = {2, 3, 4}; find (A–B) ∪ (B–A)
Solution:
A–B = {1}, B–A = {4}, (A–B) ∪ (B–A) = {1, 4}
Example 11 : If S is the set of all prime numbers, M = { x : o ≤ x ≤ 9}
exhibit (i) M – (S ∩ M) (ii) M ∪ N, N = {0, 1, 2, ........20}
Solution:
S = {2, 3, 5, 7, 11, 13, ............}, M = {0, 1, 2, ............8, 9}
(i) S ∩ M = { 2, 3, 5, 7}
(ii) M ∩ N = { 0, 1, ....., 20}
Example 12 : Find A ∩ B, if A = {letter of word ASSASSINATION}
and B = {letter of word POSSESSION}
Solution:
A ∩ B = {SSSSION} as common letters.
OBJECTIVE QUESTIONS