Question

Insert ⊆ or ⊈ in each blank to make the resulting statement true. {0, 1, 2} ____ {1, 2, 3, 4, 5}

Accepted Answer

Understand the symbols: The symbol $$ \subseteq $$ means 'is a subset of,' which means every element of the first set is also in the second set. The symbol $$ s $$ here likely refers to the symbol $$ \in $$, which means 'is an element of.' Identify the sets given: The first set is $$ \{0, 1, 2\} $$ and the second set is $$ \{1, 2, 3, 4, 5\} . $$Check if the first set is a subset of the second set by verifying if every element of $$ \{0, 1, 2\}  is in$$ $$ \{1, 2, 3, 4, 5\} . $$Since the element $$0 is in $$the first set but not in the second set, the first set is not a subset of the second set, so $$ \subseteq  is $$not correct here. Therefore, the correct symbol to use is $$ s  (or$$ $$ \in ) $$only if referring to individual elements, but since the problem compares two sets, neither $$ \subseteq $$ nor $$ s $$ fits perfectly; however, based on the instructions, the blank should be filled with $$ s  if $$the problem intends to say 'is an element of' for an element, or $$ \subseteq  if $$the first set is a subset. Here, since the first set is not a subset, the correct choice is $$ s $$ indicating the relation is not subset.

Insert ⊆ or ⊈ in each blank to make the resulting statement true. {0, 1, 2} ____ {1, 2, 3, 4, 5}

Verified video answer for a similar problem:

Key Concepts

Subset and Proper Subset

Set Elements and Membership

Notation and Symbols in Set Theory