Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of \(A∩B\) is ___________
Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of \(A∩B\) is ___________
Correct Answer: 5264
Solution and Explanation
The correct answer is 5264
Sum of all elements of \(A∩B\) = 2 [Sum of natural numbers upto 100 which are neither divisible by 3 nor by 5]
\(=2[\frac{100×101}{2}−3(\frac{33×34}{2})−5(\frac{20×21}{2})+15(\frac{6×7}{2})]\)
= 10100 – 3366 – 2100 + 630
= 5264
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Concepts Used:
Sets
In mathematics, a set is a well-defined collection of objects. Sets are named and demonstrated using capital letter. In the set theory, the elements that a set comprises can be any sort of thing: people, numbers, letters of the alphabet, shapes, variables, etc.
Read More: Set Theory
Elements of a Set:
The items existing in a set are commonly known to be either elements or members of a set. The elements of a set are bounded in curly brackets separated by commas.
Read Also: Set Operation
Cardinal Number of a Set:
The cardinal number, cardinality, or order of a set indicates the total number of elements in the set.
Read More: Types of Sets