For any two sets A and B, n(A)=15, n(B)=12, A ∩B ≠ϕand B ⊄A Find the minimum possible value of

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

For any two sets A and B, n(A)=15, n(B)=12, A ∩B ≠ϕand B ⊄A...

For any two sets $\mathrm{A}$ and $\mathrm{B}, \mathrm{n}(\mathrm{A})=15, \mathrm{n}(\mathrm{B})=12, \mathrm{~A} \cap \mathrm{B} \neq \phi$ and $\mathrm{B} \not \subset \mathrm{A}$
Find the minimum possible value of $\mathrm{n}(\mathrm{A} \Delta \mathrm{B})$.
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Key Concepts

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a counting technique used to accurately compute the cardinality of the union of multiple sets by subtracting the overcount of elements that appear in multiple sets. It provides a systematic way to handle overlaps in sets and is particularly useful in problems involving unions, intersections, and differences.

Symmetric Difference

The symmetric difference between two sets, denoted as A ? B, is the set of elements that are in either set A or set B but not in their intersection. This concept is important in understanding how the uniqueness of elements in each set contributes to the overall structure of combined or alternate set operations.

Set Intersection

The intersection of two sets consists of the elements common to both sets. It plays a crucial role in problems where overlapping elements are considered, influencing calculations involving combinations of sets, such as unions or differences.

Set Cardinality

Set cardinality refers to the number of elements contained in a set. It is a fundamental measure in set theory that helps quantify the size of finite sets. Problems involving cardinality often require finding relationships among sizes of unions, intersections, or differences of sets.

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