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A set A has 5 elements and set B has 3 elements. The intersection of A and B has 2 elements. How many elements are in A union B?
8
7
6
5
6
The number of elements in the union of two sets is calculated using the inclusion-exclusion principle, which states that the size of the union of set A and set B equals the sum of the sizes of A and B minus the size of their intersection. Given that set A has 5 elements, set B has 3 elements, and their intersection has 2 elements, the union contains 5 plus 3 minus 2, which equals 6 elements.
The number of elements in the union of two sets is calculated using the inclusion-exclusion principle, which states that the size of the union of set A and set B equals the sum of the sizes of A and B minus the size of their intersection. Given that set A has 5 elements, set B has 3 elements, and their intersection has 2 elements, the union contains 5 plus 3 minus 2, which equals 6 elements.
Set theory fundamentals form an essential part of quantitative aptitude in Indian competitive exams like RRB, SSC, and banking examinations, rooted in foundational mathematics principles.
The formula for the union of two finite sets is n(A union B) equals n(A) plus n(B) minus n(A intersection B).
The intersection represents the common elements shared between set A and set B.
The inclusion-exclusion principle prevents double-counting of elements present in both sets.
For disjoint sets where the intersection is zero, the number of elements in the union is simply the sum of the elements in both sets.
Option A is incorrect as it represents the error of simply adding the elements of both sets without subtracting the intersection.
Option B and Option D are incorrect calculations derived from improper application of set formulas.
C is correct тАФ The number of elements in the union of set A and set B is 6, calculated as 5 plus 3 minus 2.
Mastering set theory fundamentals aids directly in solving Venn diagram problems, probability distributions, and logical reasoning questions frequently tested in railway and banking examinations.