Give examples of three sets A, B and C such that (a) A ∈B, A ⊆C and B ⊈C (b) B ∈A, B ⊂C and A ∩C

step 1 Okay, now suppose we have some sets A, B, C, and given A is a subset of B, and B is a subset of

Give examples of three sets A, B and C such that (a) A ∈B, A...

Give examples of three sets $A, B$ and $C$ such that
(a) $A \in B, A \subseteq C$ and $B \nsubseteq C$
(b) $B \in A, B \subset C$ and $A \cap C \neq \emptyset$
(c) $A \in B, B \subseteq C$ and $A \nsubseteq C$.

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Key Concepts

Set Intersection

The intersection of two sets refers to the set containing all elements that are common to both sets, usually denoted as A ? B. A non-empty intersection (A ? B ? ?) indicates that the two sets have at least one shared element. This concept is essential for understanding relationships between sets where overlap is specified.

Set Membership

This concept explains the relationship where an object or a set is considered to be an element of another set. It is denoted by the symbol ?. Understanding set membership is crucial because it distinguishes between a set being a member of another set (an element) and being a subset (all elements contained within another set).

Subset and Proper Subset

A set A is said to be a subset of set B, denoted as A ? B, if every element in A is also in B. A proper subset, often denoted as A ? B, is a subset that is not equal to B. This distinction is important when conditions in problems specify whether the subset relationship is inclusive or exclusive of equality.

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