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

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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 maximum possible value of $\mathrm{n}(\mathrm{A} \Delta \mathrm{B})$.
(1) 27
(2) 26
(3) 24
(4) 25

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Key Concepts

Set Cardinality

Set cardinality refers to the number of elements in a set. It is a fundamental concept in set theory that quantifies the size of a set, which is crucial when analyzing and comparing different sets or performing operations such as union, intersection, and difference.

Symmetric Difference

Symmetric difference is the set of elements that belong to either one of the two sets but not to their intersection. It is an important operation in set theory, and its cardinality is calculated by taking the sum of the cardinalities of the two sets and subtracting twice the cardinality of their intersection.

Intersection of Sets

The intersection of two sets is the set containing all elements that are shared by both sets. It is a vital concept because many set operations and problems depend on the number of common elements, which directly influence the outcomes of these operations.

Subset Relation

The subset relation in set theory indicates that every element of one set is also an element of another set. Constraints involving subset relationships are important in many problems, as they affect which elements are counted in various set operations, such as the symmetric difference.

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