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If a set A has 15 elements and set B has 20 elements, and they share 5 common elements, how many elements are in A union B?
30
35
40
25
30
The number of elements in the union of two sets is calculated using the fundamental principle of inclusion-exclusion. By adding the total elements of set A and set B and subtracting the overlapping common elements, the total count is derived as 15 + 20 - 5 = 30.
The number of elements in the union of two sets is calculated using the fundamental principle of inclusion-exclusion. By adding the total elements of set A and set B and subtracting the overlapping common elements, the total count is derived as 15 + 20 - 5 = 30.
Set theory and foundational mathematics concepts form a core part of quantitative aptitude and logical reasoning syllabi across Indian competitive exams like RRB and SSC.
The inclusion-exclusion formula states that n(A union B) = n(A) + n(B) - n(A intersection B).
Set A contains 15 elements and set B contains 20 elements as given in the problem statement.
The intersection or common elements shared between both sets equals 5.
Option A is correct as 15 plus 20 minus 5 equals 30.
Option B (35) results from incorrectly adding the sets without subtracting the intersection.
Venn diagrams provide a visual method to solve such set theory and grouping problems efficiently.
A is correct тАФ the number of elements in A union B is 30.
Understanding set operations directly aids in solving complex probability and data interpretation puzzles frequently tested in technical and non-technical railway recruitment examinations.