Solving Combinatorics: Finding the Number of Sets with Elements from A, B, and C

  • Thread starter Thread starter Neitrino
  • Start date Start date
  • Tags Tags
    Combinatorics
Neitrino
Messages
133
Reaction score
0
Please help me with combinatorics:
I have three sets:
A with elements (a1 ……..ai )
B with elements (b1 ……..bk )
C with elements (c1 ……..cj )

Pls help me to work out how many sets ABC shall I have that contain each element from sets A, B and C

Thanks much
 
Physics news on Phys.org
You can try to simplify the problem first by considering something you can do by simple enumeration with A (a1,a2) B(b1,b2) and C(c1,c2). Then you try to generalize your results. Of course there are better ways, fancier etc but at least you have a starting point.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Meaning of "passage to the quotient"?
Replies
3
Views
453
A Anti-dual numbers and what are their properties?
Replies
1
Views
2K
Combinatorics: looking for an alternative solution
Replies
7
Views
2K
MHB Number of Elements in Finite Fields?
Replies
8
Views
2K
Combinatorics and set cardinality
Replies
23
Views
2K
I Countability of binary Strings
Replies
18
Views
2K
MHB Solve Exponential Fraction Equation for $α$ ($C$, $m$)
Replies
2
Views
1K
MHB Greatest common divisor of a and b
Replies
8
Views
3K
Technique for proving Inclusion-Exclusion principle combinatorically
Replies
5
Views
3K
Yr 10 Combinatorics -- Rearranging the letters of ABRACADABRA per this rule....
Replies
23
Views
2K

Hot Threads

Recent Insights

Back
Top