Insert ⊆ or s in each blank to make the resulting statement true. {5, 6, 7, 8} ____ {1, 2, 3, 4, 5, 6, 7}

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Identify the two sets given: $A = \{5, 6, 7, 8\}$ and $B = \{1, 2, 3, 4, 5, 6, 7\}$.

Recall the meaning of the symbols: $\subseteq$ means 'is a subset of' (possibly equal), and $\subset$ means 'is a proper subset of' (strictly contained, not equal).

Check if every element of set $A$ is also in set $B$. Compare each element of $A$ with the elements in $B$.

Since $8$ is in $A$ but not in $B$, not all elements of $A$ are in $B$, so $A$ is not a subset of $B$.

Therefore, neither $\subseteq$ nor $\subset$ is true for $A$ and $B$ in this order; the blank should be left empty or the statement is false.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Subset and Proper Subset

A subset (⊆) means every element of the first set is also in the second set, allowing the sets to be equal. A proper subset (⊂) means the first set is contained within the second set but is not equal to it. Understanding these symbols helps determine the correct relationship between two sets.

Set Elements and Membership

Set elements are the individual objects contained within a set. To analyze subset relationships, you must check if all elements of one set appear in the other. This concept is fundamental for comparing sets and deciding which subset symbol to use.

Notation and Symbols in Set Theory

Set theory uses specific symbols like ⊆ for subset and ⊂ for proper subset to express relationships between sets. Correctly interpreting and applying these symbols is essential for writing true statements about sets and their elements.

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