Question
If $X$ has 10 members, how many members does $\mathcal{P}(X)$ have? How many proper subsets does $X$ have?
Step 1
The power set of a set $X$, denoted by $\mathcal{P}(X)$, is the set of all subsets of $X$. If $X$ has $n$ elements, then $\mathcal{P}(X)$ has $2^n$ elements. Show more…
Show all steps
Your feedback will help us improve your experience
Manisha Sarker and 98 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $X$ has $n$ members, how many proper subsets does $X$ have?
Sets and Logic
Sets
How many subsets with more than two elements does a set with 100 elements have?
Counting
Permutations and Combinations
How many subsets with an odd number of elements does a set with 10 elements have?
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD