Bissoy.com
Doctors Medicines MCQs Q&A

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?

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? Correct Answer 148

Calculation:

⇒ n(A) = = 83 (A is a set of integers between 1 to 2000 and is divisible by 24)
⇒ n(B) = = 74 (B is a set of integers between 1 to 2000 divisible by 27. where 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) =  = 9

⇒ n(A∪B) = n(A) + n(B) – n(A ∩ B) = 83 + 74 – 9 = 148

Additional Information

Union 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).

Related Questions

Consider the following two C code segment. Y and X are one- and two-dimensional arrays of size n and n × n respectively, where 2 ≤ n ≤ 10. Assume that in both code segments, elements of y are initialized to 0 and each element X[i] [j] of array X is initialized to i + j. Further assume that when stored in main memory all elements of x are in same main memory page frame. Code segment 1:                 //initialize elements of y to 0                 //initialize elements X[i] [j] of X to i+j                       for (i = 0; i < n; i++)                                 Y[i] += X[0] [i]; Code Segment 2:                 //initialize elements of Y to 0                 //initialize elements X[i] [j] of X to i+j                        for (i = 0; i < n; i++)                                 Y[i] += X[i] [0]; Which of the following statements is/are correct? S1: Final contents of array Y will be same in both code segments S2: Elements of array X accessed inside the for loop shown in code segment 1 are contiguous in main memory S3: Elements of array X accessed inside the for loop shown in code segment 2 are contiguous in main memory
Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?
Let N denote the set of all non-negative integers and Z denote the set of all integers. The function f : Z → N given by f(x) = |x| is:
Let X is divisible by 2 and Y is divisible by 6 then which of the following statement is correct regarding (X + Y)? Statement 1: It is divisible by 2 Statement 2: It is divisible by 3 Statement 3: It is divisible by 4
A, B, and C are divisible by 2. C, D, and E are divisible by 9. B and D are divisible by 3 Conclusion - I 6C is divisible by 54 Conclusion - II B and D are divisible by 6 Conclusion - III 4B + 2E is divisible by 4 Which of the above conclusions logically follows/follow from the given statements?
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
Refer the below data table and answer the following Question.   2011 2012 2013 2014 2015 Company A 2000 2000 5000 2000 1000 Company B 2000 3000 1000 5000 2000 Company C 3000 2000 5000 3000 3000   For which of the following pairs of years the total exports from the three Companies together are equal? (Note: Figures given are in lakh rupees)          
A, B, C, D and E are five different integers. When written in the ascending order of values, the difference between any two adjacent integers is 4. D is the greatest and A is the least. B is greater than E but less than C. The sum of the integers is equal to E. What is the positive difference between the lowest and the highest integers?
The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers ?
Let XYZ be a 3-digit number. Let S = XYZ + YZX + ZXY. Which of the following statements is/are correct? 1. S is always divisible by 3 and (X + Y + Z) 2. S is always divisible by 9 3. S is always divisible by 37 Select the correct answer using the code given below: