2.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSAlgebra
subjects, how many students all together were in the class, who took Mathematics or physics or both,
[Ans. 73 ]- In a class of 52 students, 20 students play football and 16 students play hockey. It is found that 10
students play both the game. Use algebra of sets to find out the number of students who play neither.
[Ans. 24] - In a class test of 45 students, 23 students passed in paper first, 15 passed in paper first but not passed in
paper second. Using set theory results, find the number of students who passed in both the papers
and who passed in paper second but did not pass in paper first
[8; 22] - In a class of 30 students, 15 students have taken English, 10 students have taken English but not
French. Find the number of students have taken: (i) French, and (ii) French but not English.
[Ans. 20,15] - In a class test of 70 students, 23 and 30 students passed in mathematics and in statistics respectively
and 15 passed in mathematics but not passed in statistics. Using set theory result, find the number of
students who passed in both the subjects and who did not pass in both the subjects. [Ans. 8; 25]
[hints : refer solved problem] - In a survey of 100 students it was found that 60 read Economics, 70 read mathematics, 50 read
statistics, 27 read mathematics and statistics, 25 read statistics and Economics and 35 read
mathematics and Economics and 4 read none. How many students read all there subjects?
[hints : refer solved problem no. 3] [Ans. 3]
OBJECTIVE QUESTIONS - Write the following in roster form
(i) A = { x : x is negative odd integer, – 7 ≤ x ≤ – 3}
(ii) B = {x : x is positive even integer, 3 < x ≤ 9} [Ans. (i) –7, –5, –3 ; (ii) 4, 6, 8 ] - Represent the following in selector method
(i) all real numbers in open interval { 1, 11}
(ii) all real numbers in closed interval {–2, 3}
[Ans. (i) x ∈ A, 1 < x < 11; (ii) x ∈ A, –2 ≤ x ≤ 3} - State with reason whether each of the following statements is true or false.
(i) 1 ⊂ { 1, 2, 3 } (ii) {1, 2} ∈ { 1, 2, 4} (iii) {1, 2} ⊂ {1, 2, 3}
[Ans. (i) False, element is not subject of a set,
(ii) False. Set does’t belong to another set, may be subset,
(iii) True, {1, 2} is proper subset of {1, 2, 3}] - A = { 1, 2, 3, 6, 7, 12, 17, 21, 35, 52, 56}, B and C are sub sets of A such that B = { odd numbers}, C = {prime
numbers} list the elements of the set { x : x ∈ B ∩ C} [Ans. {3, 7, 17} - If S be the set of all prime numbers and M = {0, 1, 2, 3}. Find S ∩ M [Ans. {2, 3}
- If A = {1, 2, 3, 4 }, B = { 2, 4, 5, 8}, C = { 3, 4, 5, 6, 7}. Find A ∪ (B ∪ C)
[Ans. {1, 2, 3, 4, 5, 6, 7, 8}] - If A= { 1, 2, 3}, and B = {1, 2, 3, 4}. Find (A – B) ∪ (B – A)
[ Ans. {1, 4}]