Questions: State whether the statement is true or false. ∅ ⊄ ∅

State whether the statement is true or false. ∅ ⊄ ∅
Transcript text: State whether the statement is true or false. \[ \varnothing \not \subset \varnothing \]
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Solution

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Solution Steps

To determine whether the statement is true or false, we need to understand the concept of subsets. The empty set, denoted as \(\varnothing\), is a subset of every set, including itself. Therefore, the statement \(\varnothing \not \subset \varnothing\) is false.

Step 1: Understanding the Concept of Subsets

A subset is a set where all elements of the first set are contained within the second set. The empty set, denoted as \(\varnothing\), is a subset of every set, including itself. This is because there are no elements in the empty set that could violate the subset condition.

Step 2: Evaluating the Statement

The statement given is \(\varnothing \not \subset \varnothing\). To evaluate this, we need to check if the empty set is not a subset of itself. Since the empty set is always a subset of any set, including itself, the statement is false.

Final Answer

False

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