Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A ? B) = 80. Compute: (a) n(A? ? B) 280 (b) n(B?) 200 (c) n(A? ? B?) 120
Added by Kim C.
Close
Step 1
We know that \(n(A \cup B) = n(A) + n(B) - n(A \cap B)\). Therefore, \(n(A \cup B) = 200 + 160 - 80 = 280\). Since \(n(U) = 400\), the number of elements in \(A' \cap B\) is \(400 - 280 = 120\). Show more…
Show all steps
Your feedback will help us improve your experience
Aparna Shakti and 91 other Calculus 3 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
Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A ∩ B) = 80. Compute: (a) n(A^c ∩ B) = 280 (b) n(B^c) = 200 (c) n(A^c ∩ B^c) = 120
Sandip R.
If $n(A)=100, n(A \cup B)=150,$ and $n(A \cap B)=40,$ find $n(B)$
Sets and Counting
Cardinality
Let $A$ and $B$ be subsets of a universal set $U .$ Show that $A \subseteq B$ if and only if $\overline{B} \subseteq \overline{A} .$
Basic Structures: Sets, Functions, Sequences, Sums,and Matrices
Set Operations
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD