Show that if A and B are sets, |A| = |B|, then |P(A)| = |P(B)|. (P(X) is the power set and |A|=|B| means A and B have the same cardinality (are equinumerous)).
Added by Robert R.
Step 1
Since |A| = |B|, there exists a bijection f: A → B. This means that every element in A can be uniquely paired with an element in B, and vice versa. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Supreeta N and 58 other Algebra 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
Show that if $A$ and $B$ are sets with the same cardinality, then $|A| \leq|B|$ and $|B| \leq|A|$
Basic Structures: Sets, Functions, Sequences, Sums,and Matrices
Cardinality of Sets
Let $A$ and $B$ be finite disjoint sets, where $|A|=a,$ and $|B|=b .$ Find the cardinality of each set. $B-A$
The Language of Sets
The Cardinality of a Set
Let $A$ and $B$ be finite disjoint sets, where $|A|=a,$ and $|B|=b .$ Find the cardinality of each set. $A-B$
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD