If n(A ∩B)=5, n(A ∩C)=7 and n(A ∩B ∩C)=3, then the minimum possible value of n (B ∩C) is (1) 0 (

step 1 Hello students and this question they are given that the number of elements in A is equals to 15

If n(A ∩B)=5, n(A ∩C)=7 and n(A ∩B ∩C)=3, then the minimum...

If $\mathrm{n}(\mathrm{A} \cap \mathrm{B})=5, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=7$ and $\mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=3$, then the minimum possible value of
n $(B \cap C)$ is
(1) 0
(2) 1
(3) 3
(4) 2

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Key Concepts

Set Intersection

The intersection of sets refers to the collection of elements that are common to all the sets involved. It is a fundamental concept in set theory used to identify shared elements between groups, and is critical for solving problems where overlapping elements need to be accounted for.

Triple Intersection

A triple intersection involves three sets and includes only the elements that are present in all three. This concept is key when determining minimum or maximum possible overlaps among multiple sets, as it establishes a lower bound for the pairwise intersections involving the sets.

Venn Diagrams

Venn diagrams are visual tools that represent sets as regions, with overlapping areas indicating intersections. They help in understanding and solving problems involving multiple sets by clearly showing the relationship and common elements among the sets.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a method used in combinatorics for calculating the number of elements in the union of several sets by incorporating the sizes of the individual sets and subtracting the sizes of their pairwise intersections, triple intersections, and so on. This principle is essential for managing over-counting when sets have overlapping elements.

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