Paper 4: Fundamentals of Business Mathematics & Statistic

2.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

1. Given : A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, C = {3}, D = {0, 1, 2,.....,9]. Find :
   (i) A ∪ C, (ii) A ∪ (B ∪ C), (iii) B ∩ C, (iv) C ∩ D (v) A ∩ (B ∪ C), (vi) (A ∩ B) ∩ C,
   (vii) A ∆ B. [Ans. (i) {1, 2, 3, 4, 5}, (ii) {1, 2,....,6},
   (iii) {φ}, (iv) {3}, (v) {1, 2,......, 6},
   (vi) (φ), (vii) {1,3, 5,6}]


2. Given, U (universal) = {0, 1, ......,9}, A = {2, 4, 6}, B = {1, 3, 5, 7}, C = {6, 7}. Find
   (i) A ́ ∩ B. (ii) (A ∪ B) ~ C, (iii) (A ∪ C) ́ (iii), (A ∩ U) ∩ (B ∩ C).
   [Ans. (I) {1, 3, 5, 7}, (ii) {1, 2, 3, 4, 5,}
   (iii) { 0, 1, 3, 5, 8, 9}, (iv) {6}]


3. If S be the set of all prime numbers, M = {0, 1, 2, .....,} Exhibit :
   (i) S ∩ M, (ii) (S ∩ M ) [Ans. (i) {2, 3, 5, 7}, (ii) {0, 1, 4, 6, 8, 9}]


4. Let A = {a, b, c}, B = {d}, C = {c, d}, D = {a, b, d}, E = {a, b}.
   Determine if the following statements are true?
   (i) E ⊂ A, (ii) B ⊂ C, (iii) A ⊂ D, (iv) C ⊂ D, (v) E = C, (vi) B ⊃ C, (vii) A ~ D.
   [Ans. (i) T, (ii) T, (iii) F, (iv) F, (v) F, (vi) F, (vii) T]


5. Determine which of the following sets are same :
   A = { 5, 7, 6,} B = {6, 8, 7}, C = { 5, 6, 7}
   D = {x : x is an integer greater than 2 but less than 6}
   E = {1, 2, 3, 4, 5, 6} F = {3, 4, 5} [Ans. A = C; D = F]


6. Fill up the blanks by appropriate symbol ∈, ∉, ⊂, ⊆, ⊃, =
   (i) 3 : .....(3, 4) ∪ (4, 5, 6)
   (ii) (6) ..... (5, 6) ∩ (6, 7, 8)
   (iii) {3, 4, 5}......{2, 3, 4} ∪ {3, 4, 5}
   (iv) (a, b).....(a)
   (v) 4....(3, 5) ∪ (5, 6, 7)
   (vi) (1, 2, 2, 3) ....(3, 2, 1) [Ans. (i) ∈ (ii) ⊆ (iii) ⊂ (iv) ∉ (v) ⊆ (vi) =]


7. Find the power set P(A) of the set A = {a, b, c} [Ans. See text part]


8. Indicate which of the sets is a null set?
   X = (x : x^2 = 4, 3x = 12), Y = (x : x + 7= 7], Z = (x : x ≠ x). [Ans. Yes, No, Yes]


9. If U = {x : x is letter in English alphabet)
   V = (x : x is a vowel)
   W = (x : x is a consonant)
   Y = (x : x is e or any letter before e in alphabet)
   Z = (x : x is e or any one of the next four letters)
   Find each of the following sets :
   (i) U ∩ V, (ii) V ∩ Y, (iii) Y ∩ Z, (iv) U ∩ W ́, (v) U ∩ (W ∩ V).
   [Ans. (i) x : x is vowel, (ii) (a, e), (iii) (e), (iv) same as (i), (v) φ]


10. Given A = (x : x ∈ N and x is divisible by2)