A, B and C are three non-empty sets. If A ⊂B and B ⊂C, then which of the following is true? (1)

step 1 Hello students in this problem A B C and 3 A B are 3 non -empty sets A is subset of B and B is s

A, B and C are three non-empty sets. If A ⊂B and B ⊂C, then...

$A, B$ and $C$ are three non-empty sets. If $A \subset B$ and $B \subset C$, then which of the following is true?
(1) $\mathrm{B}-\mathrm{A}=\mathrm{C}-\mathrm{B}$
(2) $A \cap B \cap C=B$
(3) $\mathrm{A} \cup \mathrm{B}=\mathrm{B} \cap \mathrm{C}$
(4) $A \cup B \cup C=A$

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Key Concepts

Subset Relation

This concept refers to the relation where every element of one set is also contained in another. If A ? B and B ? C, then every element of A is in B, and every element of B is in C, which is essential in understanding the implications for unions and intersections of these sets.

Set Union

The union of two or more sets is the collection of all distinct elements that belong to any of those sets. When one set is a subset of another, the union of these sets is equal to the larger set. This property is key to understanding equalities involving unions under subset relations.

Set Intersection

The intersection of sets is the set of elements common to all the sets involved. If one set is a subset of another, the intersection of these sets is the smaller set, which helps in establishing equalities involving intersections within a chain of subsets.

Set Difference

Set difference is the operation that yields the elements that are in one set but not in another. This concept is used to analyze and compare the distinct parts of related sets and helps explain why differences between sets with subset relations might not be equal.

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