Let A={1,2,3,{3},{1,4,7}} . Answer each of the following as...

Let $A=\{1,2,3,\{3\},\{1,4,7\}\} .$ Answer each of the following as true or false. $$ \begin{array}{ll}{\text { a. } 1 \in A} & {\text { b. }\{3\} \in A \qquad \text { c. }\{2\} \in A \qquad \text { d. } 4 \in A} \\ {\text { e. }\{\{3\}\} \subset A} & {\text { f. }\{1,4,7\} \in A \qquad \text { g. }\{1,4,7\} \subseteq A}\end{array} $$

Let $A=\{1,2,3,\{3\},\{1,4,7\}\} .$ Answer each of the following as true or false.
$$
\begin{array}{ll}{\text { a. } 1 \in A} & {\text { b. }\{3\} \in A \qquad \text { c. }\{2\} \in A \qquad \text { d. } 4 \in A} \\ {\text { e. }\{\{3\}\} \subset A} & {\text { f. }\{1,4,7\} \in A \qquad \text { g. }\{1,4,7\} \subseteq A}\end{array}
$$

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Key Concepts

Set Membership

Set membership refers to the relation between an element and a set, denoted by the symbol ?. It means that an object is one of the components explicitly listed in the set. Understanding set membership is crucial when determining whether a specific element is part of a given set.

Subset Relation

The subset relation, denoted by ?, indicates that every element of one set is also contained within another set. It is important to recognize that a subset is a set that fulfills the condition of all its elements being in the larger set, which is different from the notion of individual element membership.

Nested Sets

Nested sets occur when elements within a set are themselves sets. This concept requires careful attention because an inner set can be an element of the outer set, and its relationship (membership versus subset) must be distinguished to avoid confusion. For example, a set that appears as an element is not automatically a subset unless its elements also appear individually in the outer set.

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