How many elements are in the power set of the empty set?

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Question: How many elements are in the power set of the empty set?

Options:

Correct Answer: 1

Solution:

The power set of the empty set contains only one subset, which is the empty set itself. Thus, it has 1 element.

How many elements are in the power set of the empty set?

How many elements are in the power set of the empty set?

Step 1: Understand what a set is. A set is a collection of distinct objects.
Step 2: Recognize what the empty set is. The empty set is a set that contains no elements, often denoted as {} or ∅.
Step 3: Learn about the power set. The power set of a set is the set of all possible subsets of that set.
Step 4: Identify the subsets of the empty set. The only subset of the empty set is the empty set itself.
Step 5: Count the subsets. Since the only subset is the empty set, there is 1 subset.
Step 6: Conclude that the power set of the empty set has 1 element, which is the empty set.

Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
Empty Set – The empty set is a set that contains no elements.
Cardinality – The number of elements in a set, which in this case refers to the number of subsets in the power set.