FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.11
B = ( x : x ∈ N and x is divisible by 2)
C = (x : ∈ N and x is divisible by 4)
Describe A ∩ (B ∩ C) [Ans. x : x ∉ N and x is divisible by 12]
- A = (x : ∈ N and x ≤ 6)
B = (x : x ∈ N and 3 ≤ x ≤ 8)
U = (x : x ∈ N and x ≤ 10)
Find the elements of the following sets with remark, if any :
(i) ( A ∪ B) ́, (ii) A ́ ∩ B ́, (iii) ( A ∩ B) ́, (iv) A ́ ∪ B ́ [Ans. (I) (9, 10), (ii) (9, 10),
(iii) {1, 2, 7, 8, 9, 10) , (iv) { 1, 2, 7, 8, 9,, 10}
- (a) Which the following sets is the null set φ? Briefly say why?
(i) A = (x : x > 1 and x < 1). (ii) B = (x : x + 3 = 3), (iii) C = (φ) [Ans. (i)]
(b) Which of the following statements are correct /incorrect?
3 ⊆ (1, 3, 5); 3 ∈ (1, 3, 5); (3) ⊆ (1, 3, 5) (3) ∈ (1, 3, 5)
[Ans. 2 nd and 3 rd are correct]
- Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9,10} be the universal set. Suppose A = {1, 2, 3, 4, 5,6} an and B = {5, 6, 7} are
its two subsets. Write down the elements of A – B and A ∩ B’.
[Ans. {1, 2, 3, 4,}; {1, 2, 3, 4}]
- Let S = {1, 2, 3, 4, 5} be the universal set and let A = {3, 4, 5} and B = {1, 4, 5} be the two of its subsets.
Verify : (A ∪ B) ́ = A ́ ∪ B ́
- If S = { a, b, c, d, e, f} be the universal set and A, B, C, are three subsets of S, where
A = { a, c, d, f}, B ∩ C = { a, b, f} find (A ∪ B) ∩ (B ∪ C) and B ́ ∩ C ́
[Ans. { a, b, c, d, f}; {c, d, e}]
- Let A = {a, b, c} B= (a, b), C = (a, b, d), D = (c, d), E = (d). State which of the following statements are
correct and give reasons :
(i) B ⊂ A
(ii) D ⊄ E
(iii) D ⊂ B
(iv) {a} ⊂ A [Ans. (i) and (iv) are correct]
- List the sets, A, B and C given that :
A ∪ B = { p, q, r, s}; A ∪ C = {q, r, s, t}; A ∩ B = {q, r}; A ∩ C = {q, s}
[Ans. A = {q, r, s}, B = {p, q, r}, C = {q, s, t}]
- If A = {2, 3, 4, 5}, B = {1, 3, 4, 5, 6, 7} and C = {1, 2, 3, 4} verify that :
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
(Hints : B ∪ C = {1, 2, 3, 4, 5 , 6, 7}; A ∩ (B ∪ C) = {2, 3, 4, 5} & etc.)
Number of Elements in a set :
