Insert ∈ or ∉ in each blank to make the resulting statement true. . 0 ____ ∅

Verified step by step guidance

1. Understand the symbols: ∈ means 'is an element of' and ∉ means 'is not an element of'.
2. Recognize that ∅ represents the empty set, which contains no elements.
3. Consider the number 0 and whether it can be an element of the empty set.
4. Since the empty set has no elements, no number, including 0, can be an element of it.
5. Therefore, insert the symbol ∉ in the blank to indicate that 0 is not an element of the empty set.

Key Concepts

Set Membership

Set membership refers to the relationship between an element and a set, denoted by the symbol '∈' (element of) or '∉' (not an element of). If an element is part of a set, we use '∈', while '∉' indicates that the element is not included in the set. Understanding this concept is crucial for determining whether specific elements belong to given sets.

Empty Set

The empty set, denoted by '∅', is a unique set that contains no elements. It is a fundamental concept in set theory, representing the idea of 'nothingness' in terms of sets. Recognizing that the empty set has no members is essential for correctly applying set membership principles.

Logical Statements

Logical statements are assertions that can be evaluated as true or false. In the context of set membership, determining whether an element belongs to a set involves evaluating the truth of a statement. Understanding how to construct and analyze these statements is key to solving problems related to sets and their elements.