Answer to Question #142097 in Discrete Mathematics for Promise Omiponle

Question #142097
Compute the number of functions f from the set {0,1,2,...; n} (where n is a positive integer), to the set {0,1}.
1
Expert's answer
2020-11-11T19:23:45-0500

Let us compute the number of functions f:{0,1,...,n}{0,1}f:\{0,1,...,n\}\to\{0,1\}. For each k{0,1,...,n}k\in\{0,1,...,n\} for the value f(k)f(k) there are two possibility: f(k)=0f(k)=0 or f(k)=1f(k)=1. Since the cardinality of the set {0,1,...,n}\{0,1,...,n\} is n+1n+1, by Multiplication Principle the number of all functions is

22...2n+1=2n+1.\underbrace{2\cdot 2\cdot ...\cdot 2}_{n+1}= 2^{n+1}.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment