Question Bank - Mathematics

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Let A denote the set of integers between 1 and 2000 which are divisible by 24 and B denote the set of integers between 1 and 2000 which are divisible by 27. How many elements are there in the set A?B?

A.
146
B.
148
C.
150
D.
144

Solution:

Calculation:? n(A) = [2000/24] = 83 (A is a set of integers between 1 to 2000 and is divisible by 24)? n(B) = [2000/27] = 74 (B is a set of integers between 1 to 2000 divisible by 27. where [x] is the greatest integer function) ? A?B = Set of integers between 1 and 1000 which are divisible by 24 and 27 both, i.e. divisible by 216.? n(A?B) = [2000/216] = 9? n(A?B) = n(A) + n(B) “ n(A ? B) = 83 + 74 “ 9 = 148Additional InformationUnion of Sets? Union of two or more sets is the best of all elements that belong to any of these sets. The symbol used for union of sets is 'U' ? i.e. AUB = Union of set A and set B = {x : x ? A or x ? B (or both)}? e.g. If A = {1, 2, 3, 4} and B = {2, 4, 5, 6} and C = {1, 2, 6, 8} then AUBUC = {1, 2, 3, 4, 5, 6 8}.Intersection of Sets? It is the set of all of the elements, which are common to all the sets. The symbol used for intersection of sets is '?'. ? i.e. A?B = {x : x ? A and x ? B}? e.g. If A = {1, 2, 3, 4} an B = {2, 4, 5, 6} and C = {1, 2, 6, 8}, then A?B?C = {2}.? Remember that n(AUB) = n(A) + n(B) - (A?B).

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